I used to work in Ann Summers for over a year so hopefully I can help. I like how informed you are about the differences! It's nice to see.
Hold-ups will always say they are hold-ups on the package, so keep that in mind. The sticky strip around the top can vary in quality so be wary of the cheaper ones, they're very likely to simply fall down. If it is just to wear for the bedroom and for a short time, hold-ups are fine. They are easier to put on, as they don't require any fiddling with fastenings, however probably won't withstand a lot of movement or, er... any sweat.
I find for longer wear, stockings and a suspender belt will always be more comfortable. They also - in my opinion - look more classical. Now, to just look good/short wear, a four-strap belt which you can buy in Ann Summers or similar stores would be fine, as it isn't necessary to hold them in place for a long time. If you do go in, you can ask them to show you how to fasten the clips. It is a case of sliding the stocking between two clips and sandwiching it in place, and can be easy once you know how.
However, for comfort reasons if it is for longer wear and to hold the stockings straight, I always recommend six-strap belts with metal clips. You can find these online or in vintage stores such as What Katie Did or Kissmedeadly. A bonus with metal clipped belts if that you can clip hold-ups as well as stockings in them which is difficult if not impossible to do with plastic clips.
Before you go into store, make sure you know her rough height (for the stockings), dress size and bra size! This can vary a lot so I find the easiest way to find out (other than asking if it is a surprise) is to check the things she wears the most. They'll be the most comfortable for her and thus often give a better idea of her size
Also, if you are buying a bra, find out which style she prefers. Balconette and plunge are the most common - balconette bras have cups which are straighter, whereas plunge ones have ones which 'plunge' in the middle. This explains it better:
http://cdn2.gurl.com/wp-content/uploads/2014/04/bratricks2.jpg I'd be happy to answer more questions if you need it.