I suggest going through ibuypower and building a system, all you have to do is select the parts, they build it and send it to you, i built a 2000$ computer through them that is a complete utter beast, i7 6700k processor (4.0 ghz, not oc yet) gtx 980ti sc , 16 gb ddr4 high speed hyper x ram, liquid cooling, z170 pro gaming motherboard, dvd rom, ssd, data drive, lighting etc etc, waaaaaay over kill for anything league related of course, but i also got a free mechanical keyboard, free mouse, and free headset aswell as free shipping and 2 game downloads.
For your budget you can still get a pretty decent machine that will max league easily, i mean i used a 13 year old computer to play league on till i upgraded that played league on max just fine, plus you can still have the benefits of some custom choices of parts and even free keyboards mouses and headsets.
If you would like i could put something together and then link it since your not very tech savvy as you said.
Whatever you do i suggest getting something that does NOT have a dedicated on board graphics, you want to be able to upgrade and expand over time, not be stuck with the on board graphics, yes some computers let you just disable that, and use a graphics card, but for 500$ i doubt there will even be a graphics card slot on the motherboard if the computer has onboard graphics.
Look at some options on ibuypower, they have already put together computers for around 500ish, or you could design your own, if you want help let me know! (i'm not advertising them just trying to help you get the best bang for your buck, i mean if you can get free peripherals why not am i right?) plus they have all sorts of deals that gets you free upgrades on graphics and processors, so i really highly suggest taking a look, they have so many deals that really gets you the best bang for the buck.
For my specific build, in total after all seasonal sales and stuff my computer would come out to be around $2400, and i only paid $1900 and got lots of free upgrades and peripherals and game downloads, no one else offers deals like that, not best buy, wal mart, target, etc etc even building the computer yourself gets contested at that point.