My sis bought this HP 2000 Notebook with 4GIG of RAM, AMD E-300 APU with Radeon graphics, dual core, for about $350. It's running Windows 8 which actually isn't all that horrible once you get used to it. Personally, I still miss the XP days but you know...
I haven't tried running FL on this thing but it ran some basic games pretty well. My shit old HP Pavilion from '06 with 1GIG of RAM couldn't even handle running Proteus (an incredibly serene but very low demand game). This comp ran it fine as well as some other simple 3d games.
You definitely DEFINITELY do not need one of those "high end" consumer knee-jerk PCs. Get something between $350 and $500 and you will be fine, trust me. All you need to do beyond that is TAKE CARE of your little computer. Some people treat their computers like trash and it makes a huge difference. Only install the bare necessities (~the simple bear necessities~) and don't let it burn itself up.