First question is... do you own or have access to a "decent" polisher? If not and you're thinking about getting one check the video below from Mike Phillips.
The only way to do paint correction is with a polisher. I would recommend a 15mm DA polisher to start with a 5" pad.
As far as pads, it all depends on how bad your paint is. If you just have some swirls, a decent foam pad will take care of them with an All-in-One polish, or a "coarse" and "fine" pad combination with a mild compound and a decent polish. I have used almost every brand out there, and right now I am using Rupes and Lake Country pads. For polishes I still have a few of the Optimum Spray polishes, but a few years back switched to Sonax products.
The
Sonax Cut and Finish is a very good one step polish, you can use that with either a medium foam pad (the Rupes Yellow) or the Rupes Yellow wool pad. My favorite is
Perfect Finish and the
EX 04-06 for one step. You need to tape all the black trim with Sonax polishes though, which is the only thing I dislike about them.
If you want something simpler, Rupes have color coordinated polishes and pads so you don't get confused and use the wrong polish/pad combo. Their Yellow is medium cut/finish, White is Final step (if necessary), Blue is coarse/compound.
The kit in the below link is pretty much what you would need to polish a car with heavy swirls.
https://www.autogeek.net/rupes-lhr15-mark-iii-polisher-kit-sonax-bigfoot-combo.html
Rupes 15mm Bigfoot, selection of Rupes pads, and Sonax heaviest compound and Perfect Finish for a 2 or 3 step polish. Not cheap, as Rupes is one of the best, if not the best in the market and the model sold in that link is the latest MK. If you're buying, I would suggest the
MKII as it is an excellent machine and it is priced down (used to be around $450 when it was released).
If you are tight on budget, even the
Harbor Freight DA long throw will work, especially since you will probably use it once. I'm adding this one, not my favorite but I think it is because I don't have much time working with one, is the
force rotation Harbor Freight polisher. It is a work horse, but you need to know how to handle it. Rotaries are awesome as well and I use them for the final step on very soft paint like Mercedes black paint, but in my opinion, not beginner friendly.
As far as waxing, you can't screw up waxing unless you do it under the sun and leave the wax for hours. Since you are in FL I would suggest you either wax your car on a monthly basis, or step up to a decent sealer or coating once you correct the paint. Remember that when you correct the paint you are, in fact, removing clear coat from your car. And our cars don't have a lot of it to begin with. The half-life of polyU clear coats is 5 years, which means that if you didn't seal or coated the car when it was brand new, and have not wax the car on a regular basis, in 5 years you will have 1/2 the thickness that was sprayed at the factory. This is measurable with a paint thickness gauge. Checking against the thickness of paint at the door jamb.
If you are going to coat, it is done right after polishing... making sure you remove all the left over oils from the polishes. After that, all you will need is a sealer, waxes that are not formulated to be used over coatings will not stick to them, it will flake off like dandruff. There are plenty of coatings out in the market... for that blue I would suggest
Kamikaze Miyabi followed by maintenance with their
Over Coat Liquid should last you for the rest of the cars existence. Or
Adams Graphene Extreme with their
Spray Coating every 6+ months. This two coatings work great on blue colors (red, green, primary colors and mix of them) For silvers the Kamikaze ISM coating would be better.
Good thing is that they provide decent "how to" videos on their websites to follow along.
Sorry for the long post, it is Friday, very slow at work... bored, lack of sleep, etc...