you mean 1080p? Have a look at a guide or wikipedia about 'monitor resolution'.
Performance costs money. You want to run AAA games at 1080p i wouldnt recommend anything less than a 1060 or equivalent.
Youll have to lower graphics settings on each game to get decent framerate at peak times.
again, look for used on ebay. whats a used gtx 970 cost?
PCPartPicker currently lists for sale 94 different models of monitor manufactured by LG, in 8 different resolutions, and 18 different screen sizes. Which one is the "normal one?"
If your monitor is 60Hz and 1080p that's a certain category of spec./performance you'll need to look at. Perhaps a GTX 1050 or 1050Ti. If it's 120Hz or 144Hz, 1440p etc. then everything changes.
What make and model of PSU do you have? If it is capable, there might be the option of a cheap-ish older card for 1080p such as a GTX 780 or 780Ti.
The more information you give us, the better chance of us suggesting something useful.