what does the PSU matter? its an Enermax Liberty 620W. I am using the built in graphics in the 2600k cpu. i'm not sure what the resolution of the monitor is. its a 19" 4:3 LCD. that should give you an idea of how old it is. its at least 4 years old, maybe more. I don't plan on getting another monitor. so if i were to buy a better video card, will my resolution in games be higher or will they remain the same due to the old monitor?
The PSU matters because discrete GPU's use additional power and we need to know your PSU can run them before we recommend them. Personally i would feel very bad telling someone to spend $300 on a GPU and have them post back that it isn't working because the PSU dosent have the juice to power it
A 19" at 4:3 is probably 1280 x 1024. This is fixed by the ability of the monitor so what ever the Max supported resolution is is the most you will get no matter what GPU you buy.
Pretty much any discrete card will be better than the Intel solution for gaming. Do you have a budget in mind ?
Ball park i would not go much higher than a 5770 or Nvidia equivalent performance card.