Never ask me for tips because I ramble! Here is what I consider a winning formula for the current Oekaki adopts:
I can't comment much on designs for species as these vary greatly, but if your goal is a successful species, follow trends - see what else is popular and then come up with your own original design that might include some of those elements. By no means copy anyone, but basically, if your design is very out-there and doesn't include anything that most people seem to enjoy, the species may fail (but it may also do just fine, and start new trends, that's just hard to tell). For example, on CS right now, horse species are very popular. Horses can be very similar but some people take their own twist on horses to make them unique to their "species." Different breeds and characteristics, etc.
As far as linearts for the designs, keep it simple. If it is super complicated and considered by many hard to draw, it'll be harder for people to get into them. You'll notice a lot of the most popular species are really in fact quite simple to draw and aren't very complicated. This goes for the actual adoptable color designs created, too. A super complicated color design is fine once and a while, but sometimes simpler stuff is more pleasing to the eye - and the person who may wish to draw that character.
The Tenvis Cats are a good example to bring up. The concept is fairly simple - a big cat who lives in the jungle with some frills. I gave a purpose to the frills so they make a bit of sense and aren't just there for looks (though they are, lol). The designs have a pattern they sort of follow, so they aren't entirely random (they have multicolored rosetted spots) and also makes variations that don't have the pattern rare and desirable (always good idea to throw in those once and a while to make things interesting and sought after). The lines aren't overly detailed or complicated, the shading isn't in the way of the designs, and they are smooth and solid.
I'm not sure what else you may want to know, but this is the general approach I take to adopts.