Well done on your purchase mate.....you'll love her after shes been tweaked a little.
The majority of people go for Stage 1 first but some do go straight for Stage 2+ or 3 dependant on what company you decide to use for the remapping. I recommend you do a little research in to what you want off a remap as the top companies all differ in the way the power is delivered. Shark, Revo, APR and Bluefin are the most popular with the 8P S3 and most have dealers nationwide.
I am Scotlands only Shark Performance dealer but also have dealerships with Loba, CTS Turbo, Milltek, BCS and many more so if you decide to go for big power in a 1'er I can supply all mods for the S3 to get it to 360bhp+. Your looking at not alot of change from £3.5k to take it to this level but only about £400 for a Stage 1 as no mods needed to run it at this power. Do be aware though that there has been occassions where clutches have failed at Stage 1 so always budget for a new clutch at this stage.
As I said before do a little research into what you want out of the remap as they all differ. There will be the usual this is better than that blah blah blah but ensure you know how each map drives. If you can find anymore S3's in your area to compare then it will make the decision alot easier. If you need any assistance drop me a PM.