Berin Lotitsch's answer is really good.
I noticed a couple of things in your question:
- You said you wanted to start using the heavy bag, meaning you might not do this very much.
- You said the stuffing is coming out of your gloves.
Try getting some decent leather gloves (no anything with padding). Dedicated boxing gloves would be great, but if this is just something you want to try today and maybe for tomorrow and be done with it, there is no reason to buy boxing gloves that you'll never use again.
Workout gloves are not the best at punching a heavy bag with, but they can prevent you from rubbing all the skin off your knuckles.
Another good option is to look at some of your local craigslist postings or eBay for a used, cheap set of boxing gloves.
I would say you could skip out on great quality, specialized gloves until you are sure you like this and plan to do it regularly.
If you decide to do it, then go back to Berin's answer.