The low angle jack plane is a great plane but was not very common until recently when Lie Nielsen and Veritas released their versions. I doubt Lynn will have that one, but he might and if he does, an antique one might be a little pricey (about the same as buying a new Lie Nielsen).
My absolute favorite and most-used plane is my Stanley #60 block plane. Mine is a rescue I bought from Lynn years ago. Lie Nielsen sells a block plane, but I don’t like it nearly as much as my #60. It’s too heavy for my tastes. (I own both.)
Depending on what you’re trying to do, I’m guessing you need to focus on 3 planes:
#4 or #4-1/2 Smoothing plane - The #4-1/2 is a little heavier and wider than the #4. The #4 is perhaps the most common plane there is. The #4-1/2 has become more popular as it is the one the Lie Nielsen is patterned after. Which one you use is just a matter of preference. They are both smoothing planes. I’ve got a #2 and a #3 and I rarely use either of them.
#5 Jack plane - This is a great utility plane. It sits somewhere between the jointer and the smoother and can be used in a pinch for those tasks too. Everything you would want to know about a #5 you can find here: https://blog.lostartpress.com/?s=jack+plane. The #5-1/4 is a narrow plane and is fairly uncommon. I wouldn’t make this one of your first planes. Save your $$ for one of the others.
#7 or #8 Jointer plane - These are big beasts. When tuned correctly they are a lot of fun to use, but it will be an upper body workout.
As for the others, you can read about the history of them here: http://www.supertool.com/StanleyBG/stan1.htm