I don't think I have any
other obvious need for a nailer, but I don't intend to use a hammer.
The walls in my house are plaster over the plasterboard with the 1"
holes in it.

I'm trying to get off as cheaply as possible here. Can I get away with
a brad nailer + adhesive? Or must I use a finish nailer (16 gauge)?

I used a 18 ga nailer w/ 2" bradnails for ours. Worked great. They're
cheap now..around 20-30 bucks at HFT and other Chinese tool sources as long
as you have a compressor. If not, you can pick them as cheap as $ 69.00 now
at Pep Boys of HFT as well...under $ 100 for both