First Basic PC Build

something like this:

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i5-4460 3.2GHz Quad-Core Processor ($179.49 @ SuperBiiz)
Motherboard: ASRock H97 PRO4 ATX LGA1150 Motherboard ($83.89 @ OutletPC)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($59.99 @ Newegg)
Storage: Samsung 850 EVO-Series 120GB 2.5" Solid State Drive ($69.98 @ OutletPC)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.89 @ OutletPC)
Video Card: MSI GeForce GT 630 2GB Video Card ($37.99 @ Micro Center)
Case: Antec One ATX Mid Tower Case ($39.99 @ NCIX US)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($49.99 @ NCIX US)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($14.98 @ Newegg)
Total: $586.19
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-03-04 21:29 EST-0500

not sure if you need monitor, keyboard/mice, and OS. If so, I can revise. Aftermarket CPU cooler is kind of a pointless purchase if you don't plan to overclock.

EDIT: something like this if you need the whole shebang: monitor, keyboard/mice, wifi, and OS

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($71.98 @ Newegg)
Motherboard: ASRock H97 Anniversary ATX LGA1150 Motherboard ($71.99 @ SuperBiiz)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-1600 Memory ($59.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.89 @ OutletPC)
Case: BitFenix Neos Black ATX Mid Tower Case ($33.99 @ NCIX US)
Power Supply: XFX 550W 80+ Bronze Certified ATX Power Supply ($49.99 @ NCIX US)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($14.98 @ Newegg)
Operating System: Microsoft Windows 8.1 (OEM) (64-bit) ($87.75 @ OutletPC)
Wireless Network Adapter: TP-Link TL-WDN4800 802.11a/b/g/n PCI-Express x1 Wi-Fi Adapter ($36.76 @ OutletPC)
Monitor: Acer S220HQLAbd 60Hz 21.5" Monitor ($99.99 @ Amazon)
Keyboard: Cooler Master CM Storm Devastator Gaming Bundle Wired Gaming Keyboard w/Optical Mouse ($27.89 @ OutletPC)
Total: $598.20
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-03-04 21:38 EST-0500

since you're asking about the first one, I assume you don't need the extra shebang. It's not like you NEED an i5 for web browsing only, but if your budget is $600, why not? Better get something a little more powerful that will last a little longer over a crappier CPU that gets outdated faster. You'd definitely be fine with an i3 or even just that Pentium G3258 for basic day to day office task (browsing, email, MS office, etc).

The PSU is a bit high for this kind of build, but with a PSU, you don't want to skimp on quality. That XFX is basically the cheapest quality PSU you will find. Dunno about anywhere else, but in the PSU world, what matters is not the brand, but the OEM (aka, the people who actually make the PSU). All XFX PSUs are actually made by Seasonic, which is a top class OEM in the PSU world (most here would say it's the number 1 OEM for PSU) so you can't go wrong with an XFX unit. Having the extra wattage on top of an i5 will allow you to stick a gaming graphics card down the line and bam, you have a decent gaming PC. Corsair and EVGA's budget (very low end) PSUs are actually third tier or lower, so not really recommended, although I guess it's fine if you are just web browsing. EVGA and Corsair makes real quality PSU at the higher end, but that doesn't belong in your budget PC.

As for the video card, no it does not need it. But, it's not a gaming graphics card or anything, it's a media card (something you would stick into an HTPC). Remove if you don't want of course, it's just something I added because it's within budget and would help free up the CPU to do other tasks in applications that may take advantage of a GPU, like Photoshop.

At the end of the day, I gave you a list that is "the best bang for your buck" that would most fit your needs within the budget. A $600 budget is a lot if all you're going to do is web browsing (you can get a prebuilt netbook for half that price that would browse the web just fine). If you don't actually want to spend your entire budget, I can put together another list for a lower budget of your choosing.

Take your time and don't rush. Make sure to discharge yourself before you start. Look up videos if you haven't already. The manual (unlike most other things) actually help, especially the mobo manual if you find yourself stuck. Don't screw in the mobo to the case too hard, you don't want to destroy the mobo. That's basically it. It should be fairly easy to do and modern mobo basically labels everything. have fun and enjoy!