OK a couple of things in that case. When you say enamels and acrylics you are talking about standard hobby paints and not some weird concoction.
The dead last step before painting is cleaning. I wipe the entire model down with an alcohol swab. I use the little wipes in the foil pack like the doc uses before he/she jabs you with the hypo. Polly S Plastic Prep is a good product too that not only cleans but takes away the static charge and lessens the likelihood of dust.
I also use Tamiya tape so that part should be OK. If you think it is still too tacky, press the tape lightly to the back of your hand once. That with lower the tack a bit more. Then, when you peel the tape off, do not pull it straight up. Pull it at 45 degrees back over itself like in the diagram below.
