Couple of semantics first just to be sure we are all talking about the same things. There are tires many people call slicks that are DOT legal R compounds. While they are legal to drive on the road, most only have two grooves to be DOT legal (and to satisfy some sanctioning body requirements that racers use DOT legal tires) and are not suitable for rain conditions. I've also heard them refered to as semi slicks, cheaters, R-compounds. Real race slicks have no grooves at all. The tires classified as competition/track on tire rack are DOT legal R compounds.
True race slicks and most R compounds not made for the rain, are not at all suitable in the wet. Liquids are not compressable like gasses, and you just ride right up on top of the water with no grooves and loose all contact. The two grooves in R compounds pretty much do nothing for wet.
And, as RFM notes, the manual says not to use slicks. Note, however, almost all the P cars I see at DEs use R compounds. I use an R compound on my track dedicated 986S. (And have a set of street tires on an extra set of wheels I use in the rain.)
Depending on the brand of R compound, you can probably get one for the same cost as a good street tire, but a slick is made of very soft rubber that, when hot, gives you more grip. So while the tire might cost the same, you will go through them much faster than street tires. Because of fast wear and the need to use them only when dry, you don't want these for everyday driving.
I tow my track car, but that's not practical for all. I have see many Porsches drive to the track towing small tire trailers - trailers specifically made to hold four track tires, and then then change them out when they get there. I've also seen some, who have short distances to drive to the track, show up with their R compounds already on.
I would not put slicks on the rear and streets on the front. The grip is going to be so different, you will have a lot of understeer.
On the size, the R compounds are sized the same way at street tires. Check 'em out on tire rack.
As for brands - everyone has their favorite. I use BF Goodrich G Force R-1s - they come as a stock size and are cheaper than some. The Michelin R compounds are very popular on the 996s I see. Hoosier enjoys the reputation for being the best - I don't know, never used them - wrong sizes for me. Kumho and Hankook are also popular and less expensive variations. Yokohama ADVAN R compound has some tread and I have seen a lotus run in the rain using those. I used them once - took a while for them to get hot.
For tire pressures, most makers of R compound will publish a hot pressure target range. I start many pounds below that range, and bleed after the first couple of sessions as necessary, and eventually get the right starting pressure to have the optimal hot pressure in a session.
I wouldn't be too quick to go to R compounds. You will learn more car control with street tires in the beginning. And the street tires can help you find the limits easier because they make noise - many R compounds do not squeal - they just let go when the limit is reached. When I go to a new track, I put on street tires to help me find the limits before swithcing over to R compounds.