How are you going to print them, in my mind that is the key question?
If you are going to develop and then just scan and archive/print using a computer then use Ilford XP2 film. It can be processed at almost any lab using the same chemicals as colour film. The real advantage is it is really really easy to scan compared to most b&w film, and scanners can use IR dust removal on the film which can often be a life saver for 35mm, yet they can't with normal silver based b&w film (e.g. Ilford FP4+).
If you are going to print in a a traditional darkroom, then I would go for something like Ilford FP4+ or if you want a bit more punch in the image try Ilford Delta 100. Both are easy films to enlarge from, and in fact are both really easy to process yourself too.
Not so sure about the quality control of Kodak film these days, I am convinced it is not as good these days as Ilford, but anyway, use Plus-X or TMAX (for a bit more punch), or BW400CN if you are scanning, assuming that hasn't been discontinued like its previous version.
Go for 100ISO if you have enough light, as 400ISO tends to get grainy fast in 35mm.
If you have the time/space get some used b&w processing/enlarging darkroom kit of eBay, it is dirt cheap these days, they real fun with b&w comes int he darkroom when you start enlarging and toning prints etc.
On the flip side, something like a Canon 5Dmk2 with Photoshop and an actual scan of 35mm film grain superinposed over an edited image can look identical to b&w 35mm scanned stright.
