I wouldn't use dishwashing detergent, Photolady, there's just too much extra stuff in there, or could be, and they seem to change the stuff so much it's hardly worth the effort to wash your dishes with the plainest stuff you can find just in order to save on photo chemicals.
How much you need a wetting agent can depend on how the water is where you are. I used to not bother, back home, but in the Midwest, forget about it. I'm actually a big fan of Rexton Hyperwet, for whatever reason, it seems to me to work better than Photo-Flo ever did for me. It's kind of like a bottle of vermouth, if you have a bar, you may as well have one: it'll last you.
I'm generally not interested in surprises when it comes to my negs.
Oh, as for chemical disposal, it really depends how much quantity you're using, and what there is for disposal in general. Kodak's got more information up than you would probably need about that on the website. Silver recovery is more worth the bother if you are doing your own prints, in general. I'm just not doing the quantity these days with any regularity, to be honest.
There *is* an intriguing fixer by Silvergrain which proposes to be a greener product (it's non-hardening fixer, I've been wanting to see if that'll help certain frustrations with scanning and all, myself: if it doesn't, I'll just use it for prints ) ...but asking on the Film board, no one seems to have tried it, yet, so I may be the guinea pig, there.
T-max developer is nice for some stuff, not so nice for others. D-76 is a nice all around type developer to start with, and good to learn the subtleties of development on. As is that Ilford stuff someone mentioned.