congrats on the car. I have on '06 convertible. Whatever I say from here on out should be considered opinion as opposed to fact, so use your own judgement when it comes to choosing products and methods of convertible top care. Having said that, I have had convertibles for 20+ years and the tops have lasted a long time. I bought a spray bottle of some kind of 'convertible top cleaner' on the first day I bought my current 06 mustang. I found that the product I bought was better designed to clean fabric tops as opposed to my vinyl top. It said it did both, it didn't seem to do anything good for me. Just realize they make two types of tops, one fabric and one vinyl and if a product says it works on both, it probably does not work well on either. I had read a lot about how you should not use armor all, and various reasons for that. I have a top that is very old and has been armor-all'd many times. It did not seem to ruin it. The stuff is a bit of a trade off though. It is a greasy coating on the material that attracts dirt. It looks good when it is freshly applied and it washes away and evaporates. If you go with that type of product, I would only do it once or twice a year. I have a bottle of 'marine aerospace protectant 303' which looks and acts like armor-all but is supposedly 'better'.
As far as the carwash, I have not taken my car through a mechanical carwash. I am sure it could be fine, but why take the chance, unless you have no access to a hose. I find it more likely to scratch up some paint or cause some other problem. You will get some leaking around the windows with water spraying from the sides. I don't know about what they call wax in a touchless carwash but I handwash with various normal carwash soaps that you find in any store. They all claim to have some kind of wax. It has not caused any weird build up on my top. I wash the car with a long handled soft brush (sold for car washing, meant to be attached to hose but I do not attach a hose), and it does a pretty good job. Avoiding sunlight will really help in the long run (several years), so a garage would be nice. I have used a custom fit car cover for many years outdoors and it has kept the car looking very good, it is just not really a choice for many people who need to use the car on a daily basis.
As you say you are new to convertible tops, it is usually recommended not to operate (lower/raise) the top when it is 'cold'. The vinyl gets stiff and could crack, it will not fold down nicely. The exact meaning of cold is debatable but probably under 60deg F. It should be ok at that temp but even there it will be more stiff than when it is like 80+.
Your car is already a few years old and the top may be separating from the frame. When you look at the top you see there are several bars going across from side to side. You may detect that the top is somehow glued or attached to these bars (or it should be). It will be tight against them when closed either way. When you open the top, to fold it down, it is originally designed to be attached to each bar. This often fails as the top gets older. The top will tend to move away from the metal frame as it is folding, and not make a nice accordion shape as it folds down. If you see this happening, be aware and get out there and use your hands to push the top into the right shape. You might just need to tap in one spot to make a nice fold. It will be obvious. If you just ignore it, I suppose it could twist up bad enough to cause a tear or something. I have never torn one this way but I have had a few that were no longer attached firmly to the frame, and it is not really the type of thing that you go buy a new top to replace, but it is a sign of age.
I had a leak in the rear window that was very hard to notice. The window is glued/bonded to the vinyl top. Sometimes this glue fails really bad and sometimes it could just get a tiny leak. I would look real carefully with a flashlight on the inside bottom of the window and feel around with your hands. (obviously with a hose or rain on the outside) The fabric they used under the window does a real good job of looking perfectly dry even when it is wet. If the leak is small you may be able to carefully squeeze a little clear silicone into the gap. (you would have to be careful doing that as you could make the opening worse) There may be a better glue out there for this job and if you find a leak, research it a bit before you try any product.
There are some drain holes around the rear wheel wells that can get clogged. There is a thread here you should find (I posted on it) search 'convertible drain' that will explain where they are, in case you need to deal with it. For now, just know that all the water that hits the small rear windows, gets dumped down into that cavity in front of the rear wheel and behind the door. It should slowly escape from under the car. It does not take much in the way of leaves and dirt (think pine needles) to clog up the drain. The first sign most people have is a sloshing sound when driving, and a wet rear seat (water under the rear seat). The cavity can fill with about a gallon or more of water and will come out into that rear seat area. There are some tips in that thread about how to get into that space with a vacuum to clean it out.
Sorry this is so long, hope it helps you or anyone else. I'm sure the car will work out fine, good luck.