For me - it depends on the contrast and the colour and how you want these representing in your paper.
[My Opinion!!]
Matt papers suit soft images better. They tend to mute the colours, and the paper itself softens edge contrast. I prefer a matt paper for mono portraits (and atmospheric landscapes). I'd recommend a lab that would do you a print on St Cuthbert's Somerset Photo Satin. If you like textured paper (I'm not keen on it for portraits as it can make the skin look weird) Fotospeed's Platinum Etching or Hahnemuhle's German Etching are 2 more excellent papers.
Gloss inkjet paper is pretty awful apart from Permajet's FB Mono Gloss Baryta which is "passable" as a gloss paper. Gloss paper can really make high contrast B&W shine (literally) but I have no gloss prints on the wall because the shine irritates me. I'd probably try a C-Type print if I *had* to have gloss, because the paper quality might be slightly better.
I think colour portraits (and some B&W if you don't want to risk matt) look best on the middle ground "Lustre" papers. Hahnemuhle's Photo Rag Baryta is a gorgeous paper, as is Canson's Platine Fibre Rag. If you're getting a print done elsewhere, watch out for someone stating "Hahnemuhle Photo Rag" because I've tested 7 papers all with the same prefix. Photo Rag Pearl is not as nice as Photo Rag Baryta for example.
If I were doing this for a client, I'd play safe and do everything on Canson's Platine Fibre Rag or Baryta Photographique (lustre papers). They're less costly than Hahnemuhle, with quality that's easily comparable and Canson papers have more often than not worked straight out of the box with minimal messing about with colour correction. Important if you're getting a lab to do it.
If I had a portrait of a young lady in B&W, I'd probably try a matt print on the Somerset paper.
If I had a portrait of "older" people in B&W (or Sepia) I'd try a matt print on German Etching - but beware that the textured look isn't for everyone.
With these last 2, you could get the prints done and if the client doesn't like them, hold on to them as samples for future clients.
Anyway - paper is extremely subjective - there's no right answer. Although every print I've done on decent paper has caused people to look at their Boots/DSCL/Max Spielman prints and seriously consider printing their own.
[/Opinion!!]