If you really want to protect and keep swirls off your paint, NEVER bring your vehicle through a wash tunnel. The "soft touch" things that whip around often have dirt and other contaminants on the brushes which spin over and over your paint job which creates the swirls. The pressure wash tunnels generally don't do a good enough job removing the road film on your vehicle. Best bet is take an hour every week or every other week and do you it yourself. If you want to spend some time doing it properly, go on YouTube and watch some videos from Dallas Paint Correction, Autolux Detailing and Pan the Organizer. Great resources that have videos that will walk you through doing everything from a wash all the way up to applying a ceramic coating.
As far as "clay and wax," the clay refers to using a clay bar. It's a bar of clay, much like play dough that you rub over the vehicle using some sort of lubricant (detailing spray, soapy water etc..) that shears off the bonded contaminants from the paint. And the wax, well, that could be anything from wax to a paint sealant to a ceramic coating.
If you take it to a detailing place they will most likely do a good job but as others stated, bringing it to someone to do a proper wash as often as you should be doing it could get very expensive. Doing it yourself not only saves a ton of cash, you can keep track of what's going on with your clear coat and paint.
I just spent 7.5 hours on my wife's CX-5 last Friday doing a paint correction and ceramic coating. I neglected it for a few years so it took a really long time. Well that and I'm a rookie... and it was my first ceramic coating that I applied. I can personally vouch for DPC Detailing's T3 coating (
DPC T3 Paint Coating - 60ml). It's a 3 year ceramic protection. The shine and gloss is shocking and the water shedding is out of this world. But it's a lot of prep work to get to that point.
I digress.
Hope that helps some.