You can buy a dedicated label printer (direct thermal is the most common, since the only consumable is the paper itself, not inks), or you can use any regular printer, ink or laser - laser is probably a bit better, though, both for cost-effectiveness and crisper barcode lines etc. 

You can print to normal paper and sticky-tape them on your packaging, or use a document pouch, or buy A4 label paper, that has 4 labels to a sheet, which is perfect for printing domestic postage labels, though there will be wastage when you don't fill a page and can't make use of the blank labels by flipping it to print on the other side, and they're not the cheapest consumable around (also make sure the adhesive is strong enough for poly mailers, I use them on satchels and they can sometimes peel off a bit easy, so put a little tape on the top / bottom edges)  - plenty of the A4 sheet labels here on eBay, but if you will be printing a lot of them, a thermal printer is probably a good investment long-term (Dymo 4XL is the most common one mentioned / recommended). 

If you use a mono printer to print an express label, or print in greyscale, just ask the staff at the PO to put express tape on it. The staff at mine give me rolls to take home and use as needed, but not all of them will do that.