What Coins Should A Begginer Be Looking For/ Purchasing?

Chute72 has eloquently covered the most important points.
I would only add that no matter how much one educates one's self mistakes will be made.
So, go to a show and make a mistake! Limit your loss by setting a limit. Say ten dollars.
Then hunt the bargain boxes for half price and "three fors" and pick out a few inexpensive coins that catch your eye. This will immediately make an addition to your grandfather's collection.

Oops! There is a second piece of advice: just see what coins 'catch your eye.' Was it bright and shiny or pleasantly darkened by wear. THEN go home and do your research on those coins which 'grabbed' you. The sooner that you train your eyes as well as acquire knowledge the better collector you will become.

Good luck, CC123.

You mentioned your disposable cash is limited; join the club. :)

When I first started collecting professionally (meaning when I first started paying for coins) a friend told me that the hobby can be very expensive. He was correct. I'm not sure how much or little you have to spend, but try to get the most for the least. This means you might have to pass up 'graded'(slabbed) coins, or accept FINE coins instead of AU's.

Don't despair though. If you're interested in modern coins, especially those that are currently circulating, you can assemble a nice collection quickly and more easily. The most enjoyable moments of the hobby are when you find something in your change that you've been looking for; you don't get that happy feeling when you 'buy' a coin.

Whatever path you choose I hope you enjoy it for a long time. As mentioned, getting educated is essential, either from books or online articles. Good luck!!