I will be playing the games at 1600x900 resolution, I will have an intel core i7-3770 (btw is that a good processor?). Some games I'll be playing are Minecraft, GTA V, Unturned and The Sims 4.
So which graphics card do you guys recommend for me, it doesn't need to be high end because I won't be playing at 1080p anyway.
Depends on your budget. The price of graphics cards are really inflated at the moment so I wouldn't recommend buying one right now.
While running at 900p is a bit unusual (as most tend to run at more common resolutions like 720p or 1080p… Although high-end gamers will go with 1440p or even 2160p aka 4K), if that's what your monitor likes… I'll go with it.
As for your processor… It's a bit on the old side, being a 3rd generation Intel Core i7 processor & the latest is 8th Gen. However, it's still fairly good & I can't knock you too much as I'm running an i7-4765T (being a 4th Gen) myself. Just considering looking at a new system if you want to upgrade your processor.
As for graphics cards, you'll likely want to run with a Nvidia GTX 1050 OR an AMD RX 560 graphics card as these are the "basic budget" models (MSRP is around $100 - $120). These will play your noted games at 1080p around the 60 fps mark under default settings, so you should have little issue with a slightly lower resolution.
HOWEVER, due to the cryptocurrency bubble, graphics cards are in high demand & prices are artificially inflated (50-100% OVER MSRP) right now. Unless you're willing to wait, willing to search for a deal (as some stores may reduce their price for those who are interested in gaming instead cryptocurrency mining… But you typically have to ask in-person about it) OR buying a brand new factory-built system, expect to pay through the nose for a graphics card.
Hope this helps!