Single Fins
Single Fins have been around for a while and are going to stay around for a long time. They are the standard these days for Longboards and in some instances Mid-lengths. Heck you might even find your local ripper rockin a 5'10" Single Fin and making it look super fun.
For an actual Single Fin Board, that does not have any side bites, the general rule is that you want in inches what the board is in feet. In other words, a 9-foot board will want a 9 inch fin. Now, some fins have a lot of surface area and others are quite narrow, so it depends on the style but that's the general rule.
As for a 2 + 1 it gets a little trickier. If you use your 9 foot as a standard jumping off point we would recommend using a 7inch fin with side bites for your all-around type Longboard. If you have a high performance 9 footer you'll probably go with a 6.5 in and if you're looking for increased stability we would say go the opposite direction and get a 7.5 inch.
A general rule of thumb is fins are either more upright and will have more pivot or they will have a lot of rake and will draw out longer arcs. Pretty much all fin designs are using a formulation of surface area and pivot or rake to achieve the desired result. So depending on the board you have to decide where to come in on that spectrum.
The other thing we will mention is to take a look at the base of the fin. The longer the base the more drive and the shorter the base the less drive, but more pivot.
One last thing to think about is it's always a good idea to put your fin in the middle of the box to start off. That way if you wish the board was a little looser you will push the fin forward. And if you wish the board was a little stiffer, and had a little bit more drive, you will push the fin back. Alright, happy fin hunting!