2003 is not old at all. In fact today's paints are remarkably resilient. Truth be told, modern paints will fare a lot better if you touch the paint a whole lot less the average enthusiast loves to.
The first thing you'll need to do is wash the car with a strong formulation specifically geared toward removing everything including the wax. You may think this is funny but Dawn is actually a good job for this particular type of wash.
Give it two good passes. Rinse it under low pressure thorough. And obviously don't use that kind of soap on the canvas top (use Raggtopp cleanser for that with a boar's hair brush or an OXO feather tip).
Soap up the car again, well one panel at a time,
and get out the Clay Bar. It's actually not clay at all but a hard play dough type plastic. break off a piece of the clay bar, flatten it so that it covers the width of your four fingers. Then rub the clay bar over the sudsy surface. You should feel a mixture of slippery then friction, that's the clay bar sliding over the clean areas then lifting away the caked-on pollutants and road grime. Use lots of lubrication, in anything you do paint related you never want to rub on dry paint. That's how you get swirls. I like to clean off the clay by dunking it the soapy bucket and rubbing off the debris before folding the clay over to work with a clean side. Rinse off the section you just clayed to dislodge any debris from the surface. Do the whole car this way. Once dry run your finger over the surface, it should be completely smooth. If not, more clay barring.
Once you've clayed the car you can do an assessment of how bad the paint looks. Most likely you'll just have to get out a quality liquid paint polish for a deeper clean. Follow up with
a sealant to fill the swirl channels. This way the surface area becomes level or 'rounded' and you don't get swirls in your shine, the sharp edges of swirls is what reflects light showing all the swirls. Let that cure overnight before you add a second layer of sealant. Then as a final touch use a liquid wax, I now avoid paste waxes as I find that there's no need to rub the paint that much, a liquid or even spray wax with enough carnauba provides more than enough gloss for a wet shine look.
As far as brands, if you are near an Advanced Auto store they carry the Griot's Garage brand which is by far your best option without having to order things from the mail. I use their clay bar exclusively (good quantity for the price) and their blue and green long nap towels for any paint work. don't use auto store microfiber towels on your paint or glass. Those are really nothing more than janitorial towels used to clean linoleum floors. If you slide your hand across the towel and feel prickly ends don't use that on paint. It's overkill.
Professional detailers that actually do a good job account for a very small % of the business. really smalll. For older cars with single stage paint those guys are a must. For this new stuff, it's not rocket science. You can do a better job than most yourself since you're not on a clock and can put more time into the job where needed. Frankly, this hobby of detailing is very expensive when you've bought all the right products of the right level of quality, and I'm not one who is a product fan boy, I buy what gets the job done at the most cost-effective price. I'd rather spend the money to have those products at my disposal rather than spending the equivalent amount for someone to do that job for me. By and large there is no such thing as a cheap detail job. An expert doesn't come cheap and most of the inital steps
do not require a professional, just someone who is paying attention. If the quoted price does seem cheap run the other way. They are most likely using cheap towels that will marr your paint -- a decent towel runs at least $3 each, car washes and budget detail shops use towels that run .30 cents each. and they are likely committing every sin in the detailing bible to get the job done asap to make room for the next job.
I would recommend you watch Larry Kossilla's series on YouTube. He works on
very high end stuff (McLaren MP4 here) and is a 964 driver himself. He sells a product line called Ammo which he personally develops. He did an overhaul of a 912 recently that was very interesting. He even had a video on waxing your car at night..I thought I was the only nutter that would do that.
https://www.youtube.com/results?search_query=drive+clean&sm=3