It seems that a lot of guys who are beginning to grow a beard (and even some veterans), have no idea what beard care products are available to them, and how those products can benefit their beards. So, I'm going to try and lay it all out here in simple terms.
If a beard oil isn't already in your beard care arsenal, you should make sure to add it immediately. Beard oils are blended concoctions made up of carrier oils such as Jojoba, Argan, Sweet Almond, etc., and usually contain some essential oils like Tea Tree and Cedarwood. These oils combine together to provide nourishment to your beard hair, while moisturizing your skin. Beard oil is not meant as a styling product, but rather a product to keep your beard and face healthy.
Like beard oil, balms are conditioning products. However, some balms are made with beeswax, while others have lanolin or butters as their main ingredients. The wax-based balms offer some styling hold. The lanolin/butter based balms are just for conditioning, but are heavier than an oil which helps tame some of the "flyaways". Wax-based balms are more firm in consistency when in their container, while the butter/lanolin based ones are more "creamy" in consistency.
These are for styling purposes only. While some may be scented, they do not have the conditioning oils that beard oils/balms have. These are great for those with beards and mustaches that just won't behave themselves. You would use these on top of the oil/balm.
While any brush or comb will work, as with anything else, some are better than others. As far as brushes go, a boar bristle type is the "go-to". It has a heavier feel when going through the hair, and helps hold things in place better than a conventional hair brush. For combs, you'll definitely want a coarse (or wide) tooth comb. The finer combs tend to snag and pull. You also want to get a higher quality comb, where the teeth have been polished and rounded to minimize the snag/pull. Well made wooden combs are great as well.
There are many products available that are advertised as a "Beard Wash". But on closer inspection, you'll find they contain the same sulphates/sulphides, parabens, and detergents that are found in the shampoo for your head. Stay away from these. You should find a wash or soap that is made without all of that crap. Your face follicles are not the same as the ones on your head, so don't treat them the same. Also, most men do not need to wash their beard daily. Unless you work in a dirty environment, washing daily is counterproductive to growing and maintaining a healthy beard. As for conditioners - if you are using an oil or balm daily, you do not need a separate conditioner in the shower.