There are many products that will help you take care of swirls and scratches. It can get quite confusing starting out for the first time. There are many different pads that are made by different manufacturers like Lake Country (LC), Edge, and Meguiars. I recommend getting some Lake Country 5.5" low profile pads. White is their polishing pad and orange is their light cutting pad. You could also get the burgundy cutting pad and yellow polishing pad from Meguiars if you wish also.
What kind of random orbital do you have? I'm assuming you have a porter cable 7424. Menzerna makes some great polishes and I use them all the time when I correct paint. For you, SIP and 106ff will take care of what you want. SIP=Super Intensive Polish. You always want to use the least aggressive combo first so I recommend a LC white pad with 106. If that doesn't work go with SIP and a white pad. I was able to correct my paint with 106 and a white pad but I used a rotary. You might have to use SIP and an orange pad, then follow it up with 106 and a white pad. It's a great combo but will take most of your day if you want perfection so plan accordingly.
You can purchase your supplies from Phil and Detailers Domain. Since you are in CT and his business is in NJ, you will probably receive your order within a couple days. Or you could buy your supplies from autogeek. If you are looking to buy pads OTC, then check out auto supply stores that supply to local body shops. The ones around me only carry meguiars pads and polishes so I have to order online if I'm looking for something different. Hope this helps and good luck with your detail.