IMO there are three types of hand saw
1. Hard point saw, mass produced, cheap (£5) and for learning perfectly useable and function well. Only real down side is that the teeth are often ground as a compromise for all of the uses it may be used for. E.g. Rip and cross cut. Equally the amount of set on the teeth is larger than a woodworker would normally set their saws which creates a wider saw cut. These factors mean that it won't cut as quickly and is not tuned for the different types of work you may do. HOWEVER, these differences when learning are not really significant and only when you start doing really fine work will you appreciate the differences.
2. Modern manufactured steel or brass backed saws where the blade is glued in. Excellent saws, will be tuned to a specific task either cross cut or rip with the number of teeth per inch adjusted for the designed thickness of wood they should cut. The thinner the wood the higher should be the number of teeth. The only down side to these saws is that if dropped and the blade becomes bowed it's almost impossible to re-tension the blade.
There is much speculation about what makes a really good saw, for any individual the decision is really down to how they feel in your hand. The majority use high quality Spring steel for the blades, and at the end of the day the differences in cut are determined by how well it's been sharpened and the users ability. I believe Lie Nielson and Veritas fall into this category.
3. Old or new saws with a folded steel of brass back. All the attributes of no 2 except if you drop the saw and bow the blade (normally when looking down the blade a distinct S can be seen along the teeth rather than it being straight) you can if you haven't damaged the blade easily straighten it out again. Any of the older saws such as Tyzak, Spear & Jackson fall into this category. The better quality saws have a brass back and also saw nuts that can be undone. The cheaper saws tended to have steel backs and rivets holding the handle to the saw blade. (Still good saws) Most can be bought on an auction site for £10~£50 or car boots for a few pounds, but almost all need to be sharpened. Modern saws include I believe Pax and certain hand made saws. The Pax saws tend to be c£100~£150 and the hand made saws £*** to reflect the time and effort involved.
IMO learning how to sharpen a saw is not hard, a few hours on uTube and reading on the Internet gives all the background you need. HOWEVER, to know when you have done it right you need to experience a really well sharpened saw to act as a benchmark. Either a friend who knows how to sharpen a saw, or the purchase of a quality well setup saw is a major factor in getting the hang of saw sharpening.
I would start out with a cheap hardline handsaw and start reading up on how to use saws and what the different tooth geometry does so you will have an appreciation of what to expect from a better saw. The next thing to do again IMO is pop along to one of the shows and try out a wide variety of saws to see and feel the differences.