Now, let's talk about the solder wick.
This is where things get interesting, yep, I've got a small canister of it and for all the use it is for the soldering methodologies I use, well..... I might as well throw it away. I've learnt of ways to not need it.
You won't get similar responses from many here, probably all to the contrary.
If I want a "clean" pad (not often necessary) I flood it with solder and suck it clean with a cheap solder sucker.
Want to suck the solder from a stubborn hole, resolder it with a low temp solder and re-suck. Rinse and repeat.
As far as methodologies are concerned: necessity is the mother of inventiveness.

Now this seem like a bit of time pissing around with molten solder and maybe it is, but it's where a temp controlled iron is invaluable as you can spend some time on pads with little fear of lifting them, but then practice makes perfect....I'm not.

By all means get some braid but I don't believe it's the greatest thing since sliced bread.
Or you could spend the money on some nice fine (bent and straight) tweezers, some small fine needle nose pliers (bent and straights) and an assortment of tips for your new Hakko.