I'm going to start analyzing the fish of the New Horizons. There is a snapping turtle which are known to be quite aggressive and are found in the river. They are nocturnal so I predict they will be available around the 4pm - 9am cycle that most bugs and fish in Animal Crossing seem to appear in. I do think they appear in summer although lets see if Nintendo wants them to be available in spring and fall. :]
The rainbowfish is colourful fish in the Indian Ocean, near the Equator. They should be around the summer time and diurnal! They are almost 12cm so...bitterling to crucian carp size.
Now the golden trout, is...judging by the name and some sources, is a protected species so expect this thing to be rare. They can be around a foot in length which I can suspect is (around) the same size as the sweetfish or turtles.
Ranchu goldfish is a special goldfish in Japan that is one of those fat ones, like they're diamond in shape. :] Despite them looking cute and all...they seem to be rare and highly standarded (that's a weird word I made up) that they will probably be rare in Animal Crossing as well. I expect them to be the smallest size for the fish.
Tilapia seem to be somewhat common to uncommon in my understanding based on some sources that explain their heavy market, not much scarcity in their natural habitats and try to predict where they appear in.

Now, they seem to be ranging from 40cm - 60cm, but really depends on the type of species! I think that they are supposed to be somewhat large...not arapaima large! I think around black bass - pike large though I'm learning more towards a black bass size. These things are diurnal so they should be available during the daytime, most likely all year or so.
Betta a is widely colourful group of fish like a guppy and they seem...$10 - $20, oh my. Ok, so they can possibly be an expensive fish. As for if they're easily farmed and they're scarcity, the IUCN Red List made them endangered so...rip you.

Now, I don't know if what type of betta they are so...

I did find that they are found in tropical climates (mostly around Indonesia) so they should be a summer fish.
Sturgeon, I wrote is an exception. I've found that they are both a freshwater and saltwater fish. I expect them to be at the estuary, the body of water that transitions from any body of saltwater to freshwater. They can grow up to 10-11 ft. so I expect them to be the largest size. Maybe they're like a king salmon. ;] I do expect them to be rare and expensive like most larger fish. Fun fact, their living ancestors that have separated into other groups are gars and coelacanths so that's interesting to see. They are, as I've seen, winter fish by my guess.
Barreleye have the eyes facing front while other fish have them at the side. These things are ugly as heck.

I'll give you this as I literally can't find much info, they appear from tropical to temperate climates in the oceans. This can mean, around summer (tropical) to temperate (which can be spring or autumn). Possibly spring - fall season? I don't know.

As for size, it depends on what that barreleye is based on. If it is based on the javelin spookfish, it can reach up to 50 cm but other species can appear under 20 cm. If it is a javelin spookfish, they can be sea bass size or larger! If it's another species, it can be smaller, maybe a olive flounder size or something.
Anchovy are tiny, hehe, seemingly 10cm - 20cm, aka 0.33 - 0.66ft for you americans.

That means, I can suspect they're not like...sea butterfly small but instead about the size of your horse mackerel or even up to a dab. Now, they appear in cooler waters, most likely some kind of winter fish. :}
If you've played Harvest Moon: Animal Parade which is no one ;-;, the Mahi Mahi is a tropical fish that is big. You'll know by it's huge forehead. They are 3ft - 5ft, I've seen. They are (most likely) the largest size for an ocean fish, blue marlin size. They should be diurnal summer fish. Like...July - September fish around 9am - 5pm.
Suckerfish are remoras! Remoras in real life latch on to larger animals (like a shark) and they both create a mutual symbiotic relationship, having the sharks be cleaned by the remora and the shark making food for the remora. If there's sharks, there's remoras. :} I predict they're summer fish, around the same time as a shark to kind of symbolize that kind of symbiotic relationship. They can be 30 - 120cm which is about 1 - 4ft. :0 That means they can be olive flounder size to a sea bass size or bigger D: