You can present in a bag in a way that's not cheesy, but I wouldn't just put prints into a bag. I have used both boxes and
Artist Portrait Cases from Rice. I like the APCs because they're different, and I only get them in 5x7 and 8x10 sizes. Each holds multiple prints so an order will last for quite some time. The packaged prints go into a gift-style bag that works with my business style (or brand, if you want to use that word). Everything is packaged as a gift. I don't like the little plastic bags, or just using a bag, because they don't offer any protection for those prints and IMO it's disappointing to spend money on portraits and have them handed over in a flimsy little bag. But what you decide to use is going to depend on what kind of presentation you want to give to your clients. Mine have spent a lot of money on portraits. It needs to look like a substantial delivery, and packaging as a gift has worked very well for me. The bags I use have my studio logo on them and are heavy enough to be reused... my goal is that they'll use them to haul things to Mommy and Me or wherever.
For bags, I've most recently used
Bags and Bows, but you might also look into
Nashville Wraps. You don't have to buy a ton of sizes... the cub and vogue style bags will fit most smaller prints and albums, because if it goes on the wall, I hope to have sold it framed. I'm not sure if they offer smaller quantity orders or not. I tend to stick with the same bag for a long time, and don't have to order very often.
You've probably already considered this, but just for everyone thinking about it: remember that whatever you decide, the cost of packaging needs to go into your pricing. I see a lot of people who are spending tons of money on packaging and their print prices can't support it