acid dipping rust removal

I'd rinse, then neutralize, then rinse again. All rinses with new/fresh/clean water. Blow dry at the end.

If you go right from the acid to the neutralizer, you'll likely wind up with a mess ;) A pre-rinse will help get the bulk of the acid solution off. Keep the part moving in the rinse and neutralizing baths too, agitation makes things go faster.

Once the final rinse/dry is done you shouldn't get much surface rust right away - once it's 100% dry, I'd begin your painting ASAP - starting with an epoxy primer or bare metal sealer.