Emmgee, Lebowski pretty much covered it.... but I'll just explain a tiny bit more (really just repeating him). Number 1, the temp regulated tip.. you'll find this in all the good hakko, JBC, etc. as well as the TS100 I mentioned that is only $50, and vert small/portable (BUT you need a good power pack to power it.... It may "work" with a 5v 500mA power adapter... but you really need something like a 19v Laptop charger that has decent amps.... this is usually something most people have in a drawer somewhere...). And as for Watts... that's one part that's a little strange.. tho may partially due with BS specs from cheap manufacturers. Theoretically a higher wattage should help a lot... but a LOW watt temp regulated JBC has been known to work when something with 5 times the watts didn't. My point being, you can't trust the manufacturer's marketing departments, at least not these cheap/low-end ones... Hakko is generally considered the cheap brand for good quality.... JBC being the industry standard (I've had real good luck with my Hakko FX-951... but about to build a unisolder to get some JBC handles).... BUT the TS100 literally has soo many people raving about it for it's price... many of these people owning JBC stations (they don't say it's better than JBC.... BUT if they're used to a JBC and still like the TS100.. it's gotta be decent).
Second, a larger tip in that situation is going to really help... and I sure hope it goes without saying, you need flux!!... there's no point in soldering without flux, it's cheap, and works magic (and while many/most good solder has a flux core... it still is so much more helpful having a flux pen and and maybe some paste). On the note of solder... you need to get a good brand... it's cheap enough anyway, but getting a no name $2-5 brand is just wasting your time... and DO NOT get the 60/40 shit... get 63/37... and I recommend having 2 different sizes... tho having VERY thin solder is much more important than having thick stuff. You need to have at least 1 roll of <0.5mm solder... 0.4 mm (0.015") is a solid choice. I use my 0.4 stuff 90% of the time... and have a rolled of 0.8mm for larger/messier stuff. If you ever solder SMD stuff, having some 0.4 (or anything under 0.5) is literally going to make it 50 times easier, and will make your soldering look so much better. When I was recommended that, it totally changed the quality of my work instantly. And get a good brand... Kester is probably the easiest to find at a decent price, tho there are others, I think Multicore is also coveted, but a little pricier, and people usually say their Kester is as good. It's also good to have a good brand of solder wick for cleaning up mistakes (Goot wick seems to be a favorite... I found some REALLY cheap on ebay.. bought from a few different stores for under $2 each... still waiting to receive it, not sure if it's gonna be real or not, but probably will do the job). If you wanna go a step further, get a cheap air station (the cheap ones are easy to find for $40-60)... I know a lot of people will say you need to invest more in a better one, and if you are serious about it, you do... but jsut for an additional tool for a hobbyist, a $50 will get most jobs done... and can help a lot when it comes to rework especially, considering you're not cooking the board with the tip of an iron on it for minutes.
But for the most part....a temp regulated (Ideally a good brand, or the TS100, which is actually open source), large tip (and not a completely round conical), good brand of 63/37 solder, and some flux.... that's what you need to do what you are trying to do.
If you need to get a better iron, and for some reason don't want the TS100 (seriously, check out the reviews on major forums like eevblog if you don't believe me)... there are other "cheap" options that aren't half bad. You can get a fake hakko handle and fake T15 tips... definitely not as good as the real thing, and won't last as long... but they are really cheap, and are temp regulated, and do work (tho prob gonna cost you more than the TS100). A real Hakko is still "cheap" compared to most others good brands.... and unloiek the real garbage stuff (and the fakes), a tip will last you YEARS (will also cost 35-50 easily), I've never replaced any of my tips on my Hakko FX-951, and it's been a few years, and def don't need to. But considering how cheap the fake ones are, and that they still get the job done, you could probably buy a pack of 15 for the price of 1, have a few options, and replace them a few times without spending much. I personalyl have a real hakko, and will be getting real JBC handles/tips (not a real unit tho).... but I did just order a fake hakko and a bunch of tips for a portable one that's to bring/lend to friends, etc. There is actually also a fake JBC station, that apparently an almost perfect copy... tho it costs I think something like $250-270... and if you were to replace the handle with a real JBC, add another $60+.... then something like $30+ per a tip (the real handle does not come with a tip at $60.... but $60 is a steal for the handle)
Anyway... I think you probably get my point. Watching those videos will help a ton... and you don't need to spend a fortune... the basics will do... but the more you plan on using it, the more worth it to get something good... you won't regret it.