First step into racing/buying advice

[tacocat123]

I just started thinking about getting into the sim racing (not actual simulation, just for fun). I first played a racing game with a steering wheel at my friend and it was awesome. I have some basic knowledge about electronics and some programming so i thought of making a DIY wheel, pedals and the paddle shifter behind the wheel. But all the guides i saw, were on a stand or something, but i don't have space for that. I'm looking for a compact wheel, pedals and a shifter setup with FFB, that can clamp on my desk, so I can move it when doing something else on my PC. Do you recommend what should I get as my first purchase? And i have a pretty low budget, 150$ max for all, so 2nd hand items are an option. I also would like to know what games should i play/purchase. My system specs are:
OS: Windows 10 64x
CPU: i5 750 2.67 ghz
Motherboard: Asus P7-H55M-SI
RAM: 8gb DDR3 133 mhz
GPU: GTX 1050 ti 4gb VRAM
480 gb ssd, 500 gb hard drive