I'm far from an expert. I bought a premade years ago, and upgraded it. Then about two years ago built my own. Both my PCs were AMD based, both in CPU and GPU. When i built my own i really wanted to go intel, but the guy helping me was an AMD fan, so I ended up going AMD. While I do think AMD is generally a really good bang for your buck, If your budget is $750 before a monitor, keyboard, mouse. I would definitely recommend going for an intel i5. Even if it's just a few bucks a year (Tek Syndicate Video), I don't like that my 8350 is an inefficient power hungry monster, that tends to get its butt handed to it by a four core i5 from intel. My next build will definitely be an intel/Nvidia based build, unless AMD does something drastically different than what they've been doing.
Take this with a grain of salt, but I would also recommend a GPU with 3 or 4 GB of VRAM. Most games to my understanding only use 2 GB. I just feel the industry is trending towards more VRAM usage. Again just my opinion.
I agree with everything mentioned prior. Also Cooler Master 212 EVO or whatever is a really good budget air cooler for your CPU.
If you want to go AMD ive seen the 8350 recenty for around $130. That coupled with a 270x or 280x would be a decent build. Again, I would recommend going with intel and the haswell chip series for upgradeability.
Don't get the cheapest PSU you can find, get something certified.
Also make sure to have some build strategy. You will end up spending more than $750 over the course of time. Hopefully you already have a monitor. When i built mine I put all the money I could into the hardware, and used crappy peripherals, and then slowly upgraded. Now i have 2 keyboards and like 5 mice, and a 360 pad. I also bought a mobo with 4 channels for ram, and upgraded from 8 to 16 (probably not necessary, but it's nice)
If the budget is super tight, I would still recommend getting an SSD and then a month later or whenever you can afford the $50-80 buy a 1-2TB HDD.
If you can be patient, and pick up the components over the next month or two, watching for sales, I bet you will do really well for yourself. Just make sure you have your build in mind.
Must my thoughts, take them for whatever they are worth.