None of these are out of the ordinary -- but I wanted to post about my favorites, the pens I think are worth your time and money, and on top of that are fun to use! You can use all these along with my Brush Lettering Handbook available here.
Here they are -- with a few other tools I often use:
Tombow Dual Tip Brush Pen - These are my go-to brush lettering pens. The dual tip is super helpful when it comes to touch ups, which no matter how much experience you have, there are always times you need to use the fine tip end to touch up your strokes. These also have awesome blending qualities, and the self cleaning is a huge plus. I have found that sometimes they dry out quicker than I think they should -- which can be a bummer for $3 a piece.
Crayola Super Tip Markers - Sure these technically are not brush pens, but surprisingly they can give you the same effect if you apply the right pressure. They aren't as durable, and won't last as long -- but you can get 50 colors for $7. They're great for practice, and to add in detail.
Micron 01 and 05 Pens - You can get quite a few sizes in these pens, but the 01 and 05 are the sizes I use most. They are waterproof, so if you are adding watercolor, you can paint right over pens. I use these most to draw banners and flowers.
Ruler - A lot of the lettering I do is bouncy so I don't always draw lines as guides. I use the ruler most when I'm working on a print and want to be sure a banner and lettering are both centered.
Gum Eraser - Any eraser will probably do, but I've found that the gum erasers are the best when it comes to smudging. Allowing proper time for the pen to dry is the most important, but some erasers I've found still smudge the writing, which is the last thing you want after you put all that time in to creating a pretty print or card.
Pencil and Sharpener - Seems like a no brainer, right? I think when you first start brush lettering, you get so swept up in the pens and technique, you forget you can go back to basics and use a pencil first! It's especially important if you're adding in some flourishes, banners or other details. I use a regular old pencil -- not a mechanical one.