I have more than a dozen multi-meters. My favorite is an analog meter from 1970s. Back then, I used to use meter as an indicator to get rough idea. It wasn't an instrument to get an accurate absolute value. On the other extreme end, I have an HP digital 6 1/2 that has been professionally calibrated. It will give me the value when that's important. I also have a clamp meter combo that I take into attic, and I also have cheap disposable kind ($<20) for working with unknowns.
The point I'm trying to make is, there is no such thing (for me) as THE nice meter. I wouldn't take my HP that's most accurate to my attic to do mains work. I also won't use analog meter to get a precise value on high impedance circuit. But if I want to see a trend, analog meter is the best. So I am kind of against the notion there IS a meter that's best.
If you are starting out, there is no reason to assume you'll be using it to work on high voltage or extremely low voltage. It's not likely there would be a need to distinguish 5 volt and 5.1 volt. Then, any meter around $50 will do. Then as your needs change, you should start adding, not replacing.
As to soldering irons, here, you will want to buy something good. I like Hakko, and you could get one for $100 or so. I also have a Chinese made ESD safe kind. I paid something like 80 dollars and it's quite good. I wouldn't use Radio Shack type or anything you'd find in harbor freifght type stores. These will make soldering job much more taxing. Soldering gun is a no-no for electronics work. That's like taking a machete to work on ship-in-a-bottle project.