A crappy saw, well maintained, will do you better than a pro saw that sits neglected and unused.
What are you going to be cutting? How often?
If I were starting out and didn’t have any specific needs that demanded a big or expensive saw, an Echo CS400 would be at the top of my list. It seems like a versatile little machine and once you open it up so it can breathe better, they seem to cut well. If it were my saw, I would drop a bar size or two (13-14”) in the interest of the sort of balance and handling I prefer.
From there, I might add a CS620 with a 16” bar for most tasks and a 24” one for the occasional task that requires more bar.
You can get away with using a bigger saw than necessary for small saw tasks much easier if you’ve hung a small bar off it. Something to consider. I was out cutting invasives a couple weeks back, mostly buckthorn and honeysuckle in the 2-4” range, and I was running an Echo brush cutter with 8”/22t blade. It was enough for what was being cut. Another guy was cutting the same stuff with me using an Echo 590/20”, and that saw was kicking his butt for doing that kind of work, largely because of the long bar being used in tight, brushy quarters. I think a light 16” bar would have made his life easier, assuming he was intent on running that powerhead for this work.
There is not much that the Echo 400/620 combo, with a sharp chain and some sitting skill/experience under your belt, could not do. Felling, limbing, trimming, and firewood cutting. There might be machines that would do the job faster, but for most of us, so what?
Having run it some, I would disagree that the Stihl 261 is some magical log saber. It is a nice 50cc saw, nothing more. I would not stretch my budget for that machine; you’d be better off with a used Husqvarna 346xp in any case, and as a bonus you’d be able to get that saw and stay within your budget.
A used 026 and/or 036 would be a very solid place to start. No objections there. Those saws are proven, bulletproof platforms.