Maybe a little late, but before even starting on the sanding of the old finish, you should wipe down the surface with wax/grease remover. If not, you could be sanding any contaminants into the surface, making them harder to remove later.
Usually before painting (after prep), I would blow off the dust and then use a wax/grease remover (wipe on/wipe off with known clean towels/rags) and then pull it in the booth. It would then get wiped down with wax/grease remover again and blown off with the spray gun and then tacked off with a tack rag(usually twice).
I dont think this project will be painted in a booth, but I hated re-doing paint jobs and more time spent in paint prep is less time re-doing.
Make sure all the wax/grease remover is wiped completely off untill it is dry. I like to wipe it down more than once as the first cleaning may just loosen some stubborn contaminants and the second wipe down should get the surface completely clean. Flip the wipe off rag to get a fresh surface to remove the Wax/Grease remover. If not, you could be just rubbing the same stuuf that came off the surface back on the surface.
Another point is when getting the wax/grease remover out of the can, don't put the rag on top of the can and tilt(swoosh) it to get the rag saturated. Pour the wax/grease remover on the the rag with out the rag touching the can(wash your hands first, too). The can may have oils, Napa stock boy boogers and who knows what else on the top of the can. If some one has sprayed some WD40/silicone near the can (somewhere along its journey to you) the WD/Silicone may get on the top of the can and be transfered to the wipe down rag and then to your surface.
Fisheye Eliminators are OK and have a purpose, but should be avoided if possible (JMO). When you use FE, You're kind of covering up one problem with another potential problem as you will "more than likely" need to use FE on any subsequent coats (a bugger when you are doing a two tone) or repainting it down the road. Most painters hate FE.(off topic, kinda- years ago, the "city boys" would "wax" their car with Rain-X and it looked great but when repainted, it would fisheye like crazy and most Wax/Grease removers (or Lacquer thinner) wouldn't budge the Rain-X. Had to use alot of FE then. I would almost bet that 10 yrs later, the finish either looked like crap or was peeling off.)
You can use tack rags on the base coat after it has dried enough. Use a gentle touch and you will be amazed at the "painting dust" that it will remove. By letting the base dry, you can also lightly wet sand any imperfections/dust down. Another coat(s) of base would be needed to get the finish back to uniform. Using wax/grease remover on the base coat shouldn't be done as it can remove the paint that you just put on.
By unfolding the tack rag, you have opened it up and have alot more surface area to get the dust off the surface. I usually would tack it off a few times (especially the smaller M/C parts) and unfold the tack rag to get a clean spot of the rag exposed for the 2nd/3rd tacking. Tack off the paint stands and the bottom of the parts also (after wax/grease remover on the backs/bottoms of the parts,too). Dont use the same wax remover rag on the top as you used on the bottoms.