I have an Accuset brad nailer. I looked long and hard to find the largest spread in brad lengths, this was it. It shoots as short as 5/8" and as long as 1.5". Accuset is a Senco brand. That is one of the very top stapler/nailer brands going. I have never had a bit of trouble with it. I would stay away from Harbor Freight brands, they are garbage. I used to work as an RV technician. A coworker bought one of their nailers. It broke after 2 days. That is not to say that HF doesn't also sell quality brand names as well. kp91 posted about an Accuset pin nailer. For a small project like yours, a pin nailer may be better.
As far as a compressor goes, you have to think about how much you will use it. Just for this project, a pancake will be adequate, but they don't produce much air. Nailers and such don't use much air, but rotary tools use a bunch. They are things like die grinders, angle grinders air drills etc. The key to getting an air compressor is CFM. How many 'cubic feet per minute' will it produce. It's frustrating to be working on a project and have to stop while the air builds back up. Good luck