You can definitely prune your trees with a bypass pruner. You'll want to add a lopper or a pruning saw to your kit once the branches you are cutting get to be more than an inch or so thick, as most hand pruners cut between .5 inch to 1 inch diameter branch.
There are lots of choices as far as brands and specifics styles of pruning tools.
I really like bahco
pruners and loppers. The steel is really good and they are made to last under heavy use. Read: Lifetime tool for the average user.
As for saws, there are even more choices! Not just brands but also lengths and and teeth density etc.
Here are a few things I've learned: Generally, a given length blade will cut a branch diameter of half the blade length. IE. A 10 inch blade will easily cut up to a 5" branch. This can probably be extended but you get the idea.
TPI stand for teeth per inch. Basically, the less teeth per inch the faster a saw will cut but it will leave a rougher edge. More teeth per inch will cut slower but leave a smoother edge. In my experience, I prefer a medium 7-9 tpi for pruning fruit trees and reserve a larger saw with less teeth (5-6 tpi) for cutting pines and firs in the forest.
The very fine saws (10tpi and above) seem to be best suited to woodworking where one might be cutting something dry and hard
All of the above details being equal, a curved saw might cut faster than a straight saw, but a straight saw is better for pruning where branches are crowded.
The Silky brand
makes very good pruning saws. The Gomboy might a good choice for you.
We also carry an excellent Japanese pruning saw
has a pretty good reputation and their pricing is lower than the Japanese saws.
Hope this helps.