I'd build it around the AMD Athlon II X4 641 Quad-Core. It's a $90 processor on the AM3+ socket..
Anyway, get that and 4GB of ddr3 ram.
Any HD will do since you probably won't install many programs..
I don't know how long you plan on recording though, so get either a large SSD (64gb maybe?) or a 1TB mechanical drive.. You'll fill up the SSD rather quickly if you're recording in 1080p and save a lot of videos.
video card is near irrelevant, but a cheap ass one like the following link couldn't hurt and would ensure higher fps on Runescape. Any card in the 55-80 range should let you max out RS.
http://www.newegg.com/Product/Product.aspx?Item=N82E16814121447
Powersupply is up to you, I like corsair brand.. You'd be good with a 350 watt but I'd go 400 just to be safe.
Now someone's probably going to post a build or whatever so they can 1-up me, even though with such low requirements it really doesn't even matter.