You're going to wan't a new processor, and usually upgrading a processor isn't as easy as upgrading your gfx card. I recommend saving some money up and putting it toward a new processor, motherboard, case exc. because it's usually easier to upgrade an entire system then to just upgrade the processor. chances are, if you just upgrade the processor, the socket type of you're new processor won't work with your current motherboard, so you'll need a new motherboard. upgrading your motherboard can mean your ram wont fit (memory standard is supported) and depending on your wattage of your power supply, you may also need a new one too. a new case may be needed also.
my honest suggestion is to look at bundles (or diy kits) on newegg.com and see if you can either get a set that includes everything except the gfx card (usually can run around $500-$700+) or get a bundle with just the motherboard, processor, and ram ($300-$500+) provided your current case and power supply supports them. also you may need a new operating system. not sure if you need a new OS license or not when you upgrade your processor and such
if you're looking at intel processors then an i5 should be more then powerful for what you need idk much about amd processors