There are a lot of good choices. I'll give you some thoughts based upon my actual use.
Color negative film:
The Kodak Portra and Ultra series of films are nice because they are all balanced the same. That is, the film base and dyes are identical across the line. This makes it rediculously easy for a professional lab to color balance all of your film and give you identical results from ASA 100 all the way up to ASA 800. Portra NC (normal contrast) gives you very smooth skin tones and colors. Portra VC gives you more saturated colors and the Ultra films give you very punchy color.
Fuji has a similar set of films in their Pro 160S (normal contrast and colors) 160C (higher contrast and color) 400H (similar to 160S) and 800Z. The Fuji films are nice if you're shooting in mixed lighting that includes flourescent lights. The Fuji films have a 4th. color layer that neutralizes (to some extent) the green cast caused by flourescent lighting, making it easier to color balance under those conditions.
Color transparency film:
Fuji transparency film kicks butt in my opinion. Astia has the lowest contrast and color saturation. It has 1/2 stop more latitude than any other transparency film I've used. It used to be my favorite chrome film, but they reformulated it about three years ago and I personally think it's a little too green now. Provia is next up the chain in terms of contrast and color. Provia 100F is my color film of choice. It's got great color and man is it sharp. Skin tones are great too. Finally, there's Velvia - uber contrast and color. Not what you want to use for photographing people, but it just drips with intense, saturated color.
I haven't used most Kodak transparency products in quite some time. The exception is Kodak Ektachrome 100 VS. I use it when I want to cross-process E-6 film in C-41 chemistry (great for wild, false colors). I prefer this film to any other when employing this technique because I like the colors I get better. Purely a personal preference.
B&W is tough because your results are influenced by your choice of developer. There are so many film-and-developer combinations that you could spend a couple of years just testing everything. My personal opinion here is that you need to do your own developing (and be religious about process control) or find a professional-caliber lab that will work closely with you to help you get yourself dialed in.
B&W is a very personal choice. I spent a couple of years doing said testing and settled on T-MAX films developed with XTOL in a rotary processor. I've used this combination for so long that I know it inside-out and backwards. I'm not taking anything away from the Ilford, Fuji, or other Kodak products. There are some remarkable B&W films available now, more in fact than there was 20 years ago.
If you're into infrared photography, try the Macophot 820 Aura in medium format. Put a Wratten #29, #89B, or Hoya R72 filter on your lens and go have some fun.
Regarding the question of just trying out some different film to get a feel for "non-pro portraiture": If you know the whereabouts of a good, professional color lab than don't be afraid to shoot a couple of different color negative films. Just make sure that the lab really knows how to print each emulsion. Some labs might only specialize in Kodak, for instance (or vice versa). If you bring them a roll of Fuji Pro 160S they may warn you that it's not their forte. They'll try mightily to correctly balance it, but won't guarrantee that the results will be as good as what they're used to dealing with. Assuming you can find a good lab, I'd recommend shooting the same subject with a roll of Kodak Portra 160NC, 160VC, Fuji Pro 160S, and 160C. Then just see which one you like best.
If you can't find a good lab in your area, I'd shoot chromes instead. You won't have as much exposure latitude, but you also don't run the risk of a lab goofing up color balance on different emulsions. E-6 is E-6 is E-6. Again, try a few different emulsions. As I said, my personal favorite is Fuji Provia 100F, but try a roll of Fuji Astia 100F and a couple of the Ektachromes and decide for yourself.
People who do stupid things with dangerous substances often die! -me