Ah, this discussion brings back fond memories of the Allied Radio catalog and Weller 8200 soldering guns of my mis-spent childhood, and the smell of rosin core flux wafting hither and yon. <sigh> And I was amazed when the radio shop guys I haunted in my youth showed me how to make my own tips out of 12-gauge copper house wire. A miracle!
You can't go wrong with Weller - I still have two W-TCP units (and what is I think my original 8200 somewhere) but replacing the tips or replacing the whole shebang got way too spendy for my pocketbook. Sadly, the Asian units are quite good and at about $25 per complete station they last a year or so and can be thrown away without much remorse.
Check eBay and search for '936B' and 'soldering' and a bunch of pretty decent clones of the Hakko solder station will turn up. Thermostatically controlled and adjustable, fast heating and mucho cheap-o.
The tips are cheap also - but with the new-fangled lead-free solder they need to be a bit hotter and oxidize faster so don't last as long as you'd like. If you can stay with 63/37 solder you'll be much happier.
Regarding NiCad batteries - there's a rather corrosive but miraculous flux (used to be marketed under the name 'Sal-Met') that will almost solder anything to anything with tin-lead solder. I've used it with great success on battery terminals. just clean the bejeesus out of it after soldering to neutralize the flux. The 'Sal-Met' flavor of flux now seems to be marketed by Esab as All-State #509: Soldering Flux for Aluminum and Dissimilar Metals.
Just my $.02
Stu