What are the
first 3 products I should buy?
I take by your thread title that you do realize that you will be buying more car care products down the line, but are just looking for a starting point.
I agree with the general concensus that the first product you should buy is a good automotive specific wash. For OTC, my preference would be Meguiar's NXT. It is widely available (at least here) at the discount stores and auto stores alike. My second choice would be Mother's California Gold. It might be my water, but Meg's Gold Class would be way on down the line of preferences.
Straying from the crowd a bit, but my second product would actually be a group of products...tools. Again going with OTC products...
1) A quality wash pad, mitt, or sponge. There are several threads discussing preferences of product, but the general belief is that either a
100% cotton chenille mitt/pad, or a real (not synthetic) sheepskin mitt, or a sponge like a sea sponge (not readily available OTC) or a grout sponge.
2) Various tire and wheel brushes - W@lM@rt has a nice soft wheel brush in it's Detailer Line (look for 2-tone blue) and
3) a drying tool like an Absorber or a WaffleWeave drying towel. Viking has several nice towels which should be available at the auto stores.
My third product would be a QD. Try any of the OTC brands available...Eagle One Wipe-n-Shine, Meguiar's Quik Shine, Mother's Showtime.
Another option (but not a replacement) for the QD could be one of the Spray Waxes like EO's WAUD or Mother's FX Spray Wax.
That should be a quick and clean (not dirty

) start. You can expand and grow your collection from there. Check out some of some of the sponsors here and supplement or replace your OTC products as you decide.