I tend to get level 5 fishing on day 5. In order to get it on day 3 you need to look out for Fish Taco, Trout Soup, Dish O' the Sea, Fish Stew, Shrimp Cocktail, or Chowder, which will up your fishing level (for that day, not forever). Check the Salon every day, Gus can sell various dish of the day, which one could potentially be a fishing buff. Plus, Willy always sells Trout Soup.
Mountain Lake is best for Bullhead and Largemouth Bass. Beach is a little harder unless your fishing level is up one. Bullhead is pretty smooth catch compared to other fish out there.
You can get Catfish at fishing level 1 (I have), but I also haven't. It just highly depends. Save gold for trout soup, that could help with catching catfish.
Also, day 3 isn't the only day it rains either. If I was unlucky on day 3 (which I have been unlucky), I'll pick another day to get the catfish.
I would fish to get enough gold for the fiberglass rod, so you can put bait on it. Willy will also sell different fish bait every day, including but not limited to catfish bait.
I tend to fish aggressively for the fish bait maker at fishing level 6, which outside a few random fish, usually catches whatever fish you put in the bait maker.