Aircraft Paint Stripper WILL soften and mar the plastic so be real careful, however, it is the fastest and easiest way of removing several coats of old paint.
Any paint stripper will do the same, part of the active "strippint" agent is Methyl Ethyl Ketone (MEK) as well as other nasty agents, it will even soften the gelcoat on fibreglass.
You can use it though, you just have to be extremely careful with how you use it. The problem is that if you aren't familiar with how quick and how much to use, you'll more than likely find it 5 times the amount of hazzle as compared to just getting a D/A sander and some 80-120 grit paper.
Using a D/A sander, (Dual Action) with sand paper in the long run will be the fastest way you can do it. I would recommend using 80 grit to cut the top two or three coats of paint, and then stepping up to a 120 or 180 for the final coat. At that point you would switch to 220 to prep your base to accept primer.
If you do not have access to a D/A then you need to get the old elbows loosened up and attack it by hand. Get a block sander and using the same process as with a D/A, however, I would probably switch to wet sanding for the 220.
I would recommend that you block sand or D/A to remove some of the old paint, but don't get too neurotic about it. The key thing that you are going for is smooth surface. Then wet sand it with 220 to give you a good surface for the primer.
Primer to use? Well depends on just how scratched up you end up. If you work carefully with the D/A you should be able to go with low or medium fill primer, shoot two med / hvy coats and wet sand to get ready for paint. If on the other hand you really scratch it up, go with a high fill primer and red cap.
Primer for the most part is Lacquer Primer, i.e. it uses Lacquer
Thinner to thin / clean up. It is the "standard" primer most people use.
There are other primers such as Epoxy primer, and Primer Sealer.
Epoxy primer is expensive but has outstanding bonding and resistance properties. Unfortunately it is also usually a NON-SANDING primer. Meaning that it doesn't have a lot of fill material, and it is forumulated such that within 24-48 hours you can top coat it with paint without having to wet-sand it to accept the top coat. This is the primer to use when you know that the item to be painted is essentially perfect and just needs the primer to have the paint adhere to.
Primer Sealer, is formulated to SEAL the base upon which it is applied over. This is especially helpful for painting over unknown paints / surfaces. Certain paints and primers when applied over other paint or primers can "liven" or "activate" the base coat. Sometimes that will cause crazing, cracking or even lifting off the base coat. This is especially noticeable when you paint a Lacquer Thinner Based product over an Acrylic Enamel product. This can also happen when you paint over fibreglass, certain types of filler, plastic, rubber etc etc.
For this job I would recommend you use a Medium fill Primer Sealer. It will give you something to wet sand to give you that smooth surface you want, while allowing you to not have to worry about the prior coats of paint or even the plastic interfering with your final paint coat.
As you wet sand your primer sealer, go ahead and use Red Cap to fill any imperfections or surface irregularities, if you are worried that the red cap might interfere with your paint, shoot a final coat of primer sealer and give it a scuffing to accept the paint. Then paint to whatever you want, lacquer or enamel.