I couldn't really get by doing what I do with just three saws but I think for most people a 50cc class saw should be primary. Most of the firewood in the world likely gets cut by a saw in this class. This should be a good quality saw. Then I think on the high end you should have a large saw (90cc or larger). This saw could be an old 40 lb relic if it isn't something you're going to use a lot but will need sometimes. If your going to use it a lot, this should also be a modern, good quality saw. Then I think it is very useful to have a small saw. (very small). There are lots of times when I use a Stihl 018. This little saw with its .043 gauge chain works great for limbing, cutting big bushes, pruning, cutting the odd piece of lumber (cordless saw) etc. The "small saw" can be a cheap one. A new little saw can be had for under $200 and used for a lot less. I fix up and sell Poulan 2000 saws all the time for $45 and they work well as the small saw.
With those three, a person can deal with about any cutting situation. Now start filling in the gaps.