First...
aboard, and I hope you continue to enjoy this great hobby!
Other than things like interiors, I try mightily not to do any serious painting until after basic construction is done. It's too hard to deal with any filling and sanding of seams -- not to mention glue from attachment points of other parts, and things like scrapes and fingerprints -- without having to basically go back and redo significant parts of the painting. And, as you've discovered, once something does go wrong, it's really hard to match touchups and repaired areas.
All that having been said...there are frequently things that need to be painted first. You can minimize the grief by making sure to scrape any paint away from the actual surfaces that are being glued, since the paint will prevent the glue from being able to essentially 'melt' those surfaces for a good strong bond. (Ironically it will usually dissolve the paint and make a squishy mess, but won't get a good bond from the plastic.)
The other trick, when using glue near paint is necessary, is to use tape, Blue-Tack or Silly Putty to try to mask off and protect painted areas. This comes with its own potential hazards -- since glue leaking or wicking into or under any of those things will cause more mess.
Last, you didn't mention what kind of glue you're using or how it's applied...but brushes or applicator nozzles, or anything that gives a little bit more precise control with dispensing the adhesive, can help fend off those headaches.
As to the bad fit of the base...we've all been there. A lot of us test-fit parts and assemblies as we build...but it's easy to forget those last added bits, or things like bases, where bad fit or other surprises can put a dent in otherwise-satisfactory projects. The only real cure for that is to always try to be thinking a step or two (or three) ahead, to try to think what might go wrong before it does. The good news is, that will come with experience.
Hope any of this is helpful. If you've got specific problems or questions, by all means let 'em fly. There's a pretty good 'brain trust' on this forum, with lots of different interests and levels of experience, so good advice is seldom in short supply.
Cheers 