CPU for basic web browsing and online games (BTD5, Town of salem, EX)

I'm assuming that it's 250USD, not AUD or CAD. Otherwise, my recommendations will be completely off the mark.

AMD A10-7700K (around 100 bucks give or take, 4 cores, and is a K CPU for unlocked full overclocking ability.)
Gigabyte GA-F2A88XM-D3HP (found it on American Newegg for like 68 bucks.)
G.Skill Sniper series 2x4GB 1866mhz ram, model no. F3-14900CL9D-8GBSR (about 40 bucks, I personally run this ram kit. It's good.)
Antec VP450 (for all your power needs, I can personally vouch for how reliable these are. Usually 35-40 bucks)
Take a look around Newegg and Amazon for cheap cases. Newegg's house brand Rosewill makes some pretty decent cases, like the FBM-01 that comes completely kitted out with fans, and has good airflow for how cheap it is. I have one of these as well, though I don't use it much anymore.)

I know this puts you damn near 300, but the beauty of this system is 1.) the lack of need for a dedicated gpu, but has the performance of a low- to mid-range dedicated gpu; 2.) if you want more power later, you can look up basic overclocking guides and shell out another 30-ish bucks down the line for a better and quieter cooler; 3.) that Antec PSU is actually a 550W power supply, underrated and branded as a 450W, so you can stick a graphics card in there later and still have enough juice from the psu; and 4.) it's a quad core. Keep in mind it's not a true quadcore because AMD CPU's of this architecture function more like having 2 cores hyperthreaded than 4 true cores, but nonetheless, it's a quadcore.

If it definitely has to be under 250, you can get a single 4gb stick of ram now for under 20 bucks, and get another matching stick later. RAM is only ever going to get cheaper as time goes on. Also, the FM2/FM2+ platform has no upgrade path. If later, down the line, if you want (to quote Jeremy Clarkson) MOAR POWAHHHH, you're going to need a new motherboard and CPU. The recommendation above is the best CPU for the FM2+ socket. The best motherboard for the FM2+ platform in my book is the MSI A88XM Gaming or A88X-G45 Gaming (different form factor, essentially the same board), only because I had one myself and it overclocked like a beast. It is, unfortunately, a $155 motherboard.

I will continue not to recommend anything from intel, because you gotta pay the intel tax to get anything from intel with any semblance of performance. For gaming, as of writing this reply, intel CPU's are far superior to AMD's offerings, but it comes at a cost.

Your other options at this budget would be to piece together a PC of ancient hardware from ebay offerings (my favorite), or to find a crappy HP/compaq/whatever best buy tower PC that probably has a dual core CPU, 2gb of ram, a hard drive you don't need, and a copy of windows that's been neutered.

Sorry for the wall of text. Feel free to ask if you have more questions.

Cheers!