I think matted print looks more special.
I usually dry mount it to a museum board (2 ply) sized about 2 to 3" larger than the edge of the print. Then temporary tack that to a backer board. Then put an over mat then put it in to a sleeve.
Another way I do it is with "photo corners." Then photograph easily comes off. I never do it with B&W prints I spent time in darkroom. But if the photograph was machine printed, I do it this way. If they get damaged or wrinkled, I can easily reprint them.
If the recipient doesn't like what I did, he/she can easily remove the mounted photograph and do whatever else. I usually have enough scrap board around in smaller sizes, so the cost is non-issue for me.
I usually cut boards to standard size. That way, the recipient can easily find ready-made frames. If special size is necessary, I usually do the whole thing and frame that myself. It has to be a special present to a good friend.