A few things to consider. First, Logging has been the most dangerous profession for as long as I can remember. 2nd, a chainsaw is akin to a standard push mower that has had the wheels and deck removed, a pair of handles attached directly to the engine along with a LOT more blades. I'm 48 now. I started running chainsaws when I was around 13. With the exception of a few years during and after college, I've always heated with firewood. I do volunteer work on disaster sites. I will NOT climb a tree with a chainsaw and have no desire for a top handle machine.
IF you really want a chainsaw, by all means go buy one, but buy a helmet and a set of chaps to go with it and WEAR them. See if you can find a training course by Stihl or Husqvarna. DON'T come on here asking for advice and assume that the members here think you are some wimp who doesn't know their top end from their bottom. With very few exceptions, members here are extremely helpful and want nothing more than to help you. Mostly, we want to keep you out of the hospital which is a VERY real possibility regardless of how tough a person is.
As far as that bush goes, there are a few options. One option is obviously a chainsaw. Another option is a reciprocating saw (ie sawzall) with a tree blade. If you have a large gas powered string trimmer with a straight shaft, you could also buy a Forester brush blade for it, and it will easily cut through what you have. Another option is an ax or hatchet. The limbs in your picture appear to be around 3" to 4" across which is pretty small. That's 3 or 4 well placed hits with an axe for each one. Another really good option for that is a pruning saw. Corona makes a folding 10" saw that's excellent and costs less than $25 on Amazon. If I needed that tree removed and none of my saws were available, I wouldn't bother waiting until I got one of them operational. I'd likely grab an ax and my Corona and go cut it down by hand. I'd likely take most of it down with an ax, and then go back and cut everything closer to the ground with the hand saw. Shouldn't take more than 30 minutes.
As far as the stump, you could grind it or you could dig it up and use an ax to cut the roots. You could also rent a small compact backhoe or mini which would make the digging process MUCH faster.