Reddit mentions of X-TRONIC 3000 SERIES - MODEL #3010-XTS VARIABLE POWER 70 WATT SOLDERING STATION WITH EXTRA HEATING ELEMENT AND SPONGE, BRASS SOLDERING TIP CLEANER INCLUDED WITH A SUPPLY OF FLUX IN THE BOTTOM OF THE CAN

Soldering irons with adjustable heat are usually pretty good. I bought this one and its great. I also use Kester solder 60/40, and have never had problems.

Regarding the Oscope, the best budget option is the DSO nano. It has large enough bandwidth to be good for audio. If you want something more robust with a better reputation and built in multimeter, the TPI 440 is an excellent option. Its available for $250 shipped from www.kiesub.com .

Do you mean something like this pencil solderer and this solder?
I've never done any soldering before so I'm not quite sure what I need to do. Would watching guides on youtube be enough for a simple soldering job like this?

Sure thing. Like with most hobbies, it's when you first get into things that is the most expensive. Thankfully, it's not that bad to get started.

First off, you'll need some solder. That's a meltable metal used to join two things together. This roll will last you for several projects: https://www.amazon.com/gp/product/B000G36BYU/ref=oh_aui_search_detailpage?ie=UTF8&psc=1

Next, you'll need a soldering iron. I've been pretty happy with this one: https://www.amazon.com/gp/product/B00KS8XA2Y/ref=oh_aui_search_detailpage?ie=UTF8&psc=1 but people swear by Weller. I'm not sure I'd get that 40 watt one that's a similar price on Amazon though, I tend to keep mine at a fairly high power and it works nicely that way.

(I'm assuming you have a Harbor Freight near you for the other stuff. They're pretty common) Then you'll want a multimeter. This is your cheapest option, and if you check your junk mail you might have a coupon for a free one: https://www.harborfreight.com/7-function-digital-multimeter-90899.html but it's lacking in audible continuity (translation: if you want to check that two points are electrically connected, it beeps if they are). This might be worth the extra money: https://www.harborfreight.com/11-function-digital-multimeter-with-audible-continuity-61593.html. Or if you really have some money burning a hole in your pocket, get one of these: https://www.harborfreight.com/5-in-1-digital-multimeter-98674.html - that has some extra features that really come in handy, but aren't totally necessary either.

That covers the most expensive tools, but there are still a few odds and ends you'll want.

• Wire stripper: https://www.harborfreight.com/7-inch-wire-stripper-with-cutter-98410.html
  
• Wire cutter: https://www.harborfreight.com/4-1-2-half-inch-diagonal-cutters-40695.html for the little things, and https://www.harborfreight.com/6-in-diagonal-cutters-63816.html for some of the bigger stuff
  
• Electrical tape - pretty common stuff
  
• Wire - maybe something like this? I wouldn't go much smaller than 16AWG. BTW, higher AWG means smaller wire. https://www.amazon.com/TUOFENG-Silicone-Wire-Feet-black/dp/B075L5Y6L9/ref=sr_1_6?ie=UTF8&qid=1519509184&sr=8-6&keywords=hookup+wire+16+awg