The Fx6300 will NOT BOTTLENECK YOUR RIG... it will do just fine with GTX950 and even with GTX960 or R9 380. Things start to look tight only at GTX970/R9-390 range, and even that can be solved by overclocking
Also, the i3 6100 might get you some extra FPS at 1080p in many cases, but the general PC usage and multitasking will be quite better with the Fx6300 so there's a trade off that you need to think about.
trying not to be a fanboy here i will say that both CPUs are ok and have their pros and cons and upgrade Paths, for the Fx you can go for an 8core or you could try overclock. For the i3 you get all the skylake (with all of the advanced features like USB 3.1 and DDR4) CPUs and if you upgrade to a "K" version you can also overclock that upgraded chip in the future... But be aware that overclock needs decent motherboard, psu and aftermarket cooler at least, and also involves some risk no matter how safe anybody tells you it is.
Even being an aging technology i would take the Fx path, since for the money of that i3 you can get the Fx6300 + Hyper 212 evo and try a moderated overclock in the future, so you have a possible upgrade path right there. Also the extra cores while still not superb will indeed provide a little better multitasking and general PC usage... At the end of the day the Vishera's are still decent chips since the CPU advance it has not being that great since the Sandy Bridge era up until and including Skylakes, and the advantages of the Skylake platform (DDR4 mainly) are far from being a "must" for 2016 and will share the market with older (DDR3 mainly) features for a while.
As for the Graphic card, the 950 its a great budget choice, i wouldn't suggest anything lower for 1080p, maybe the R7 370 if you have a 900p (or lower) monitor but also want to connect your rig once in a while to a 1080p TV.
a good rig could be:
- Fx6300
- MSI gaming 970 (you can also go with Asus M5a97 R2.0, don't go with 990 chipset unless you want to SLI/CF)
- 8gb DDR3 1866 (1x8 should be the best choice, since 2x8 config will allow 16gb 1866mhz that 4x4gb can't provide)
- GTX950 (look at the zotac Amp! edition, its a great card, if not, try to overclock the card you get up to the amp! stats)
- 1 TB HDD 7200 (WD caviar blue could be fine. No SSD needed, but if you can you should get one at least 120gb)
- EVGA 500w PSU should be fine even overclocking CPU and GPU, even if you add another 8gb of ram, it will fell short if you want to upgrade your GPU to anything except for GTX 960, but for now its more than OK.
- any used ATX Case, even from some time past will be a nice deal, look for coolermaster 335 or some similar model that will be able to take an hyper 212 evo. This will let you save some bucks or maybe get a higher end case at the price of a lower end one
that will cover the "budget gaming rig" and will be also a decent "budget multitasking/edition PC", there are some cheap few extras that can provide a lot of performance for less than $100
You can also add:
- 8gb more of ram (16gb its the double of what's needed today for 1080p gaming and that will futureproof your rig a little)
- a 120gb SSD (this is not a must, but a modern PC needs to have one to be enjoyable)
- Coolermaster Hyper 212 Evo (that's the king of low budget overclock, with this bad boy you can go up to about 4.5ghz)
at the end of the day keep in mind that both CPUs will perform great for the most part of home usage, but this are budget pcs and that will be exposed from time to time and the "expiration" date of both rigs (with no updates) should be around 2020