@MrMeanie, welcome, and congratulations!
On a three piece get suspender buttons, whether or not you have belt loops. The belt loops will be covered by the waistcoat when you wear it. Don't wear a belt and the vest together.
As to whether to have belt loops at all, here are my thoughts. One can wear the waist a bit looser with suspenders than with a belt. So, if you think you will wear it as a two-piece, and stll want the suspenders, do not get belt loops. If you would wear it with a belt as a two-piece, then get belt loops.
When it comes down to details like this, we are talking about any three piece suit, rather than a wedding suit. Given that, I would certainly look beyond this thread for input, as many people will have something to say on the subject. Lots of experience, and expertise, dwell here - sometimes in the same person! Get a wide swathe of opinions, and sort out from that what you think makes the most sense.