Shoes for Indoor Rock climbing
Outdoor Gear Lab wrote a pretty good article on the subject here:
Quoting from this article:
If you are just starting out then you probably want a more comfortable, versatile, all-around shoe. Don't go for the aggressive down-turned shoes. Go for something that is not too tight and does not cost much. Shoes that close with Velcro are great because you can get them on and off fast. But a comfortable pair of lace-up shoes can be great as well.
Agressive downturn shapes are very helpful if you're climbing intermediate / advanced routes (5.10 / V4 and up). The shape of the shoe will bunch your toes together, and also will fit tighter. This will improve your ability to stand on smaller holds. Also, a downturn makes it easier to hook your toes on holds on overhanging routes.
But if you want to stick with a more comfortable shoe, that's OK to. Plenty of strong climbers will wear more comfortable shoes. If you find your toes slipping within the shoe as you try to stand on a hold, or you find the edge of the shoe flopping when you try to stand on a small hold, you'll know its time to switch to something more "agressive'.
Velcro will be more convenient to take on and off when you're switching between climbing and belaying (which you'll do a lot in the gym). But, most velcro shoes tend to be at least a little agressive.
Fit tends to be very personal, and most of the better shoes are made of leather, and actually stretch quite a bit, so even experienced climbers may have to buy more than one size if they switch brands. (The stretching tends to mold the shoe to your foot, so its really a desirable quality)
EDIT: I didn't address your question very well. Most beginner / comfort shoes are either 1) Inexpensive entry level shoes 2) traditional climbing shoes I think that nearly all "comfort" shoes (and traditional ones) are lace ups. You'll want a lace up shoe where all your toes lay flat. Also, you'll want to avoid an asymmetric, downturned shoe. Those two things (asymetric, downturned toe boxes that force your toes to curl up) are signs on an uncomfortable, more agressive shoe.