Howdy!
I personally prefer a plunge router. It is not necessary, but if you can find a good plunge for the right price, go for it. For me it is for these 3 reasons:
1) It is much easier for cutting out inside areas in wood. You can alternately drill out an area, and then take a fixed router to cut afterward.
2) I find it just easier to set the height of the bit.
3) I do woodworking outside of arcade cabinets, and other projects have needed the plunge feature.
I still haven't built a router table, but I have seen homemade ones before. They seem easy enough to build.
Jigsaw should be fine for cutting a CP, but be sure to get or make a straight edge guide for any straightaways. Also, get a heavy duty cutting blade, jig blades tend to bend when they overheat. You will get a ton of recommendations for a circular saw though, because it is just the easier route for straight cuts.
I haven't cut acrylic with a router yet, but everyone seems to do fine with it.