Hi there BKSinAZ,
Welcome to the forums.
In general, any "hobby brand" cements, putties and paints will work with your models. Often it comes down to personal preferences and you will get many opinions on which is "better".
For cements, I favour liquid cements over "tube" types. I generally use Tamiya extra thin liquid cement and whichever one of several "heavier" liquid cements I have within reach eg. Tamiya "standard", Revell "Contacta" or one of my old favourites from a previous modelling lifetime, Faller "Expert" (don't know if this is still available - mine's 20+ years old and still usable) The Tamiya and Revell are brush-on types in jars and the Faller is in a squeeze bottle with a needle-point applicator.
For putty, I use Squadron green putty (other people will have their own personal preferences)
For paints, I favour acrylics, and use Tamiya, Gunze and Vallejo. Again, this is a personal preference thing - some people use "enamel" paints exclusively and avoid acrylics - it's just a question fo finding what you like.
An airbrush is certainly advantageous, but is by no means a necessity. We all started out with the humble paintbrush, and there are people out there whose brush painting skills are nothing short of amazing.
It pays off in the long run to buy good quality brushes - if you take care of them they will serve you well for many years. The cheap "dollar store" brushes in bulk on a card just don't cut it. They fray, they shed bristles and usually don't have a good point on the brush. When you buy quality brushes, it's the point that you're looking (and paying) for. I'd suggest a size 4, 2, 0 and 000 to start with - this range should cover most modelling tasks. With a good 000 sable hair brush (and a steady hand) you can paint eyebrows on a 1/35 scale figure.
However, that being said, it may not be wise to splash out on a set of Winsor & Newton Series 7's just yet.
When you buy your brushes, if possible, select each one yourself, check the point, don't buy it if it has a mis-shaped point, frayed or bent bristles.
Now, having said all that... It's easy to get caught up in all the details, and the endless debates over which paint/glue/putty/airbrush is better - at this point you should just try a few simple kits, get a feel for building and have some fun.