Yes, most solder has flux inside it these days, but it's in a limited amount, between 1% and 3%.
The flux is designed in such a way that it turns liquid or somewhat liquid before the actual solder melts, and falls down on the area where you want to solder (the wire lead, pcb pad, whatever metal your tip is near) and attacks the surface removing oxides and preparing the surface for the actual surface.
Especially if you have a cheap unregulated solder iron, or if you use too high temperature on the tip, when you're done using solder wire it can often happen that due to the high temperature some of the flux inside the solder wire that's left on the spool has poured out because it melted faster than the actual solder, let's say maybe a centimeter or so.
That's why you'll see advice like you see in that Avionics soldering series of videos linked above , to cut a cm or so of solder from the beginning of the spool whenever you start soldering (to make sure there's flux right at the beginning), or to cut a small piece of solder from the spool and use that (so that when you work again with solder from the spool, there will be flux right at the beginning of the wire)
Flux is seriously very important and really helps soldering, and if you look around you can find liquid flux relatively cheaply - I bought a tiny 50ml bottle of no-clean flux for something like 3$ from a local store in my country, big distributors sell 5-10ml flux pens for 5-10$ or something like that.
A European distributor sells the same flux i use cheaply, from a couple of dollars + about 5$ shipping :
http://www.tme.eu/en/katalog/#search=topnik+flux&s_field=niski_prog&s_order=ASC&id_category=100484&visible_params=1677%2C2%2C1625%2C1682%2C909%2C849%2C436%2C1597%2C74&used_params=2%3A84346%3B909%3A6811%3B1677%3A10968%3B You can then go to a pharmacy or a vet and buy a few syringes and needles and take a few ml from the bottle whenever you need to control the amount of flux you apply on boards or leads.
Here, pharmacies sell syringes and needles no questions asked, but in other countries if there are some stupid laws (maybe they think you're drug addict), a vet shouldn't have problems giving you some needles that aren't suitable for humans (larger in diameter or something like that). But you can do without syringes, in worst case scenario you make a hole in the bottle cap with a regular needle and use some tape to close the cap when you're done.
After flux, In order of importance I'd say the technique of soldering matters - you don't put solder on the tip and then bring it to surfaces unless you have separate flux to apply beforehand on the surfaces that will end up soldered (because putting the solder on the tip burns out the flux inside the solder).
A tiny bit of solder to the tip is ok, to make transfer of temperature more efficient.
If flux is used, there's whole soldering tehniques like "drag soldering" and others explained in the videos above, where you put flux on the tip and drag the tip over contacts and the solder is sucked on the metal contacts and solders the parts ... but again, separate flux is essential for this kind of soldering.
Then you have the soldering wires, I explain in the link from my post above differences between some solders. I prefer 63/37 and then 60/40 . Lead free solder needs more temperature to melt and it's harder to visually determine if your soldering was proper when you're done, so with mains soldering irons it's harder to properly solder. Get a good quality solder with lead in it.
So quality flux and quality solder are cheap and good investements that will last you long time. Buy them from an authorized distributor, not eBay or Chinese stores. Digikey, Newark , Mouser in US, Farnell or TME.eu in Europe , these are the big known sellers.
As for soldering stations, see the suggestions I made here about cheap soldering stations you can get from eBay :
https://linustechtips.com/main/topic/608140-good-solder-iron-under-60-cad/They're clones of old Hakko soldering station designs (like clones of Hakko 936) but that old design is so simple and cheap to reproduce, even these clones are decent enough, good value for the money.