Here's a link to B&H who sells every type of film available on the market: https://www.bhphotovideo.com/c/buy/Roll-...
Adorama.com is another great store/site to buy film.
The black & white films on the market are by Kodak and Illford.
T-Max film (iso 100 & 400) has very tight grain structure and good contrast. The ISO 400 is a good general purpose film.
Trix-X - This is an iconic old-school film. It has a much larger grain structure than T-Max, but it has a look to it that it coveted by artists and professionals alike.
Pan F (ISO 50) Use this film when you need zero grain and/or to print large. At only ISO 50, your exposures are going to be much longer than iso 400, which is why most use tripods with this film.
HP5 (iso 400) which is a great general purpose film. A fairly wide contrast range, HP4 and HP5 are good for when you've got a contrasty scene. HP5 can be pushed to ISO 1600 and ISO 3200 if you need faster shutter speeds.
Illford's Delta film is similar in grain to Kodak's T-Max. Unlike HP4 (iso 125) or HP5 (iso 400) - Delta has a much narrower contrast range of 5 stops. This means that it won't retain detail in the shadows and highlights in high-contrast scenes. It's a fantastic film to use on flat, overcast days where it'll boost the contrast of the scene, providing a snappier look.
Fujifilm - I've never used Fuji's Acros, but I have always heard good things about it.
As your first roll, go with an ISO 400 like HP5. It's a fairly forgiving film with a decent latitude.
All of the above-mentioned films require B&W processing which you can do yourself, or send it out. B&W processing costs more than color processing due to fewer people using it. There are chromogenic B&W films that require the same processing as color print film. Films like Illford's XP2 is a film that uses color (C41) processing which is cheaper and takes less time. Down side is that since the image is being printed on color paper, there will always be some kind of color cast to the images. Often there is a magenta color cast, but if you go to a decent photo lab, you can discus options with the technician.
B&H also sells a bunch of other films that I've never used. I think Rollei film is re-branded Agfa Pan. If so, the Rollei ISO 25 is a superb film for landscapes and still life work (or anything else that can be taken with long shutter speeds).