I'm not sure about your… Game setting and fps thingy… But uh. I'll just share what I know. First PC, totally out of everybody's league. Its customized into god only knows ways and you have work to do since it gets over heated and such. So that's a big no for a gamer. The second PC you've mentioned, its capable of running all kinds of games on it. How? The specs 16GB RAM, 1TB HDD and its clock speed explains it all. Desktops are generally powerful than laptops. So this one's definitely better than your first choice.
Now, the problem. Operating system. Why was it removed in the first place? I'll be honest with you, I wouldn't actually buy any of those PCs above since they're both modded in some way. You never know what kind of mods people do to a PC. Plus you're looking through online. It'd be wiser to not buy it than buy it and get cheated. What I'm saying is, his modifications might have impact over your PCs performance as soon as you install an Operating System. You need to make sure that you're installing the right operating system to your PC. Make sure that your hardware is compatible with your operating system which you install. If it doesn't compete with the operating system which you choose to install, then that'll ruin things. Like, your game may load, but, you may have graphical problems or audio problems. Distorted audio or zero audio in worse case scenario. Blank screen but only audio might occur too. These are the possibilities you might wanna consider before you make your decision. Cause sometimes, some hardware can't be supported by the OS.
What does that mean? Like, your sound card, might be supported for windows XP and Vista. But when you choose to install windows 7 or 8, there won't be a compatible driver available for download. When that happens, you can't do anything but plug out your sound card and buy a new one which adds up to your budget. These are the problems you might face when installing operating system to a PC without an operating system. How do I know? Been there, done that. I've tried to force downgrade my windows vista pre-installed laptop to windows XP. It worked all fine and fast as expected. But, no sound card support for windows XP. So I had to use that laptop as windows XP without sound. The sound card in my laptop could not support windows XP. If I needed sound really bad then I should remove the sound card and buy a new one that's compatible with my motherboard. So I upgraded it straight to windows 7 of course, lol.That's how I know.
I'm not trying to give you false hopes or anything. Just making sure you know what you're doing and you're being cautious about it. IF by any chance his specs were right, even then, you wouldn't know which operating system he set the hardware to compete with. Or at least, he should've stated it under the description or operating system information. However, you can try your luck with windows 7. I may not have helped you with the exact information you need, but I sure did provide something useful.