I currently have an old road bike set up with a Suntour Blaze drivetrain, 7 speed in the back and 2 in the front. For a while now my chainring/crank set has been a little off, the chainring is a little bent and moves back and forth while I'm pedaling, but I haven't had the money to change it out. If I buy a new chainring set, does it have to be the same brand or model or can I use, say, a Shimano or SRAM setup? and does anyone have any recommendations for what I should get?

Not an expert, but any crank should work. Some specify number of gears for the back, but its slightly silly. I know 10 speed crank works with 8 and 9 speed chain and cassettes. 7 speed chain might not like a 9 and 10 speed crank, so replace chain at same time with an 8 or 9 speed chain (I am fairly certain a 7 speed chain is wider than 9 & 10, it might be same as an 8).

I would replace BB at same time as crank. I would also make sure your crank is tight before buying replacement. They can loosen over time and will look like they lobe in and out as you pedal.

You can straighten the chainring with an adjustable wrench. That's free.

If it fails for some reason, chainrings are much cheaper than entire cranksets.

Maybe the crank bolt is loose, or the bottom bracket bearings are loose. If you hold the pedal with your hand, do you feel any side-to-side wobble ? How about the other pedal ?
Let's figure out what the actual problem is first.