Build for a 10 year old

What's the max budget?

I would get a better GPU if possible : http://pcpartpicker.com/part/msi-video-card-r7250x1gd5
Keep in mind that the motherboard might come with older BIOS which won't support that CPU, so it might become a problem if you don't have a supported Haswell CPU to use for updating the BIOS.
EDIT: I also found some cheaper RAM: http://pcpartpicker.com/part/mushkin-memory-996995s

I think that will play games better especially with the 2400 Mhz Memory ( APUs benefit from the faster memory ) .

PCPartPicker part list: http://pcpartpicker.com/p/66NNBm
Price breakdown by merchant: http://pcpartpicker.com/p/66NNBm/by_merchant/

CPU: AMD A10-7850K 3.7GHz Quad-Core Processor ($173.98 @ OutletPC)
Motherboard: Gigabyte GA-F2A55M-S1 Micro ATX FM2+ Motherboard ($44.69 @ Newegg)
Memory: G.Skill Ripjaws Z Series 8GB (2 x 4GB) DDR3-2400 Memory ($81.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($53.99 @ Amazon)
Case: Cougar Spike MicroATX Mini Tower Case ($29.99 @ Mwave)
Power Supply: EVGA 500W 80+ Certified ATX Power Supply ($34.99 @ Newegg)
Monitor: Acer G226HQLBbd 60Hz 21.5" Monitor ($109.99 @ NCIX US)
Keyboard: Cooler Master CM Storm Devastator Wired Gaming Keyboard w/Optical Mouse ($29.99 @ Amazon)
Total: $559.61
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-05 14:32 EDT-0400

Take a look,USAFRet:
http://pcpartpicker.com/p/kbRGdC
Much better and if you can throw in an extra $5.59,you will have an excellent build.

What abut mine?

well, considering the gt730 is gonna be basically useless at the native resolution of that acer monitor, why not ditch a gpu and use the integrated gpu until funds become more plentiful. then you can show him how to upgrade a rig, which is similar to outright building one but not exactly so.
the 70 bucks saved on the vid card could be put towards a better HD/ssd/cpu/mobo/whatever. you could save a couple bucks and droper to gskill ram (just glanced real quick). 1600mhz 1.5v ddr3

Alternate Build that Will handle games much better ,

PCPartPicker part list: http://pcpartpicker.com/p/36NNBm
Price breakdown by merchant: http://pcpartpicker.com/p/36NNBm/by_merchant/

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($59.49 @ Amazon)
Motherboard: Gigabyte GA-B85M-D2V Micro ATX LGA1150 Motherboard ($59.79 @ Amazon)
Memory: G.Skill Sniper Series 8GB (2 x 4GB) DDR3-2133 Memory ($74.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($53.99 @ Amazon)
Video Card: Sapphire Radeon R7 260X 2GB Video Card ($114.99 @ Newegg)
Case: Cougar Spike MicroATX Mini Tower Case ($29.99 @ Mwave)
Power Supply: EVGA 500W 80+ Certified ATX Power Supply ($34.99 @ Newegg)
Monitor: Acer G226HQLBbd 60Hz 21.5" Monitor ($109.99 @ NCIX US)
Keyboard: Cooler Master CM Storm Devastator Gaming Bundle Wired Gaming Keyboard w/Optical Mouse ($27.89 @ NCIX US)
Total: $566.11
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-05 14:40 EDT-0400

Damn... So Newegg is a no-go? http://www.newegg.com/Product/Product.aspx?Item=N82E16820226395&nm_mc=AFC-C8Junction&cm_mmc=AFC-C8Junction-_-na-_-na-_-na&cm_sp=&AID=10446076&PID=3938566&SID=
If so, what sites can you use?

From what I understand, modern CPUs have a graphic core almost as strong as the GT 730. The 730 may be a good upgrade for a PC with an old CPU, but for a new PC, I wouldn't take anything cheaper than the Radeon R7 250X (Don't forget the X at the end.), previously known as the Radeon HD 7770. See here why: http://www.tomshardware.com/reviews/radeon-r7-250x-graphics-card-review,3747-4.html

You may save a bit if you take only 4GB of RAM - 8 is for heavy multitasking or heavy gaming of the kind that this PC is not capable of anyway. Remember that you can add another stick of 4GB in a few years, when 4 won't be enough anymore.

You are very lucky ... I hope I live long enough to do the same w/ my grandsons....... did this w/ my kids when they were 8 and by the time they were 12, kept trying to reduce my role to a strictly "advisory nature" . The would ask questions but once they knew it was their box, they did all the screw turning and cable connections the 2nd time around with me chipping in a few comments such as :

-make sure ya grounded
-RTFM
-wash your hands
-RTFM
-Might wanna put the cooler on 1st before you put MoBo in case
-RTFM
-Better check the manual and see if that's where they want the RAM.

By the way .... that's Read The FAT Manual

One of the best parts of the experience however you might consider ...as when once the parts are here, these talks will be impossible ...

Do the parts selection with the kids .... I did a "Aunt Barbara wants me to do a build for your cousin Robert, he's your age, what do you think he will like ?...... we looked up systems requirements for games they both played, read posts on THG and came up with a parts list based upon what we read. Of course the case got the most attention and of course it hurt my eyes . I closed with, "when it comes can you help me build it" ?

The next part was fun too. While we waited fro the Brown trucks to arrive, I suggested that we d/l the manuals. We made a 3 ring binder for all the manuals and read thru them. Gave them yellow highlighters and pointed out important stuff. When we did the build, as we approached each task, he'd ofte remember the picture of say installing the RAM and turn to the appropriate page.

Was asked to put together a build recently for a friend that had little kids .... didn't need GFX card at this point but wanted to be able to add 1 or 2 down the road..... It also had Mom limitations .... no gaudy cases must fit in living room decor (mostly white) and not over $750 w/ OS .... you don't have a MoM beating you up about appearance so the case switch will get ya right in range

This is what I gave him .... next XMas he can get a GFX card, be fine for now w/ IGP

CPU Intel Pentium G3258 3.2GHz Dual-Core $59.49
Motherboard MSI H97M-G43 Micro ATX LGA1150 $89.99
Memory G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 $78.98
Storage Seagate Barracuda 1TB 3.5" 7200RPM $53.98
Case Phanteks Enthoo Pro ATX Full Tower $109.99
Power Supply EVGA 750W ATX12V / EPS12V $49.99
Optical Drive Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer $16.98
Operating System Microsoft Windows 8.1 (OEM) (64-bit) $89.98
Monitor Asus VS239H-P 23.0" $158.99
Keyboard Logitech Wireless Touch k400 w/Touchpad $29.99

That's odd, the link takes me to PCPartPicker and then to Newegg.

2400 now same price as 1600
http://www.newegg.com/Product/Product.aspx?Item=N82E16820226345

A slightly different build.

PCPartPicker part list / Price breakdown by merchant

CPU: AMD FX-4300 3.8GHz Quad-Core Processor ($88.29 @ Amazon)
Motherboard: MSI 970A-G46 ATX AM3+ Motherboard ($67.99 @ Amazon)
Memory: Mushkin Stealth 8GB (2 x 4GB) DDR3-1600 Memory ($65.99 @ Newegg)
Storage: Western Digital RE3 1TB 3.5" 7200RPM Internal Hard Drive ($46.99 @ Amazon)
Video Card: XFX Radeon R9 270X 2GB Double Dissipation Video Card ($164.99 @ NCIX US)
Case: Apevia X-SNIPER2-RD ATX Mid Tower Case ($49.99 @ Mwave)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($50.99 @ Amazon)
Optical Drive: LG GH24NSB0 DVD/CD Writer ($13.99 @ Newegg)
Total: $549.22
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-05 15:29 EDT-0400

I must admit,that's a nice build. ^

Maybe this:

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($59.49 @ Amazon)
Motherboard: ASRock H81M-HDS Micro ATX LGA1150 Motherboard ($54.99 @ Mwave)
Memory: Mushkin Stealth 8GB (2 x 4GB) DDR3-1600 Memory ($65.99 @ Newegg)
Storage: Western Digital RE3 1TB 3.5" 7200RPM Internal Hard Drive ($46.99 @ Amazon)
Video Card: HIS Radeon R7 260X 2GB iCooler Video Card ($109.99 @ Amazon)
Case: Apevia X-SNIPER2-BL ATX Mid Tower Case ($49.99 @ Amazon)
Power Supply: Antec 450W ATX Power Supply ($34.99 @ NCIX US)
Optical Drive: LG GH24NSB0 DVD/CD Writer ($13.99 @ Newegg)
Monitor: Gateway KX2153 Abd 60Hz 21.5" Monitor ($89.99 @ Newegg)
Keyboard: Cooler Master CM Storm Devastator Gaming Bundle Wired Gaming Keyboard w/Optical Mouse ($27.89 @ NCIX US)
Total: $554.30
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-05 16:03 EDT-0400

Not the biggest fan of this case. I remember you saying you had the 210 before, but I still think it's a better idea to just get the windowed version for the 210 and add some LED fans to it. I think it would look nice, not sure about a ten year old though...I would think as long as it glows it would look cool.

Maybe without the optical drive and with a cheaper case,like the Rosewill Galaxy-01,and a better monitor,it would be good.

One of what?