Flux: 1. Get good quality, name brand supplies (applies to solder and wick too). Names like Kester, MG Chemicals (they sell their Rosin 835 in smaller containers, so it's very handy for hobbyists IMHO), Multicore, Indium, AIM (American Iron and Metals), and Chemtronics (wick) for example. Chip-quik is also good for both gel flux and solder paste. You'll save yourself a lot of aggravation this way.
2. Liquid v. gel/paste, it's more application & personal preference. For example, some prefer gel for drag soldering, as liquid can run all over if not controlled. Toss say a refillable brush pen into the mix, such as a
Bonkote BON-102, and the control is attainable to the point personal preference may take precedence. There's also needle bottles, brush bottles, refillable flux pens (plastic or felt tips), or even dipping a brush into a well of flux. Lots of methods to apply it that can control the covered areas.
3. In the case of BGA, I'd also recommend liquid for the same reason as
the_memristor (flows under all of the balls). This assumes you won't be using paste, but actually use a reballing jig. The jig and solder balls aren't expensive, but it's a PITA IMHO (but I see BGA as a PITA in general, especially for hobbyist use).
Other:4. Solder paste does have a shelf life and storage conditions, so read the datasheet from the manufacturer.
5. Vacuum pen and tweezers will help you place and manipulate the chip. You don't need to go crazy here, just a cheap pen and a couple of tweezers, say #5 & #7 can do a lot, and not just with BGA.
6. Round nozzles will do for most anything. Check youtube for some videos on BGA using a hot air station for technique. Specialty nozzles have their place, but are primarily time savers, not absolute necessities. Shields help, which you can make out of disposable aluminum pie plates, turkey pans, ... you can find in kitchen sections of your local superstore (dollar stores are great for these).