Now, I do have a lot of brush markers already... (Obsessed, remember?) Maybe, though, you want to give brush lettering a whirl, and you don't have a brush marker yet.
The Crayola markers (both the bigger ones and the slimmer, Super Tips-not shown) are pointed enough to get both thick and thin lines, similar to brush markers.
The trick is (as with a brush marker), to use very light pressure on the up strokes, and heavy pressure on the down strokes. You will get the pretty thick/thin line variation, even if you are simply writing in your own handwriting. Also, as you make the down strokes, putting more of the side of the tip onto the paper will result in a thicker line. For the thin upstroke, use more of the point.
Write slowly. Hand lettering is more like drawing than like writing.
I'll be posting about some more of my favorite brush markers for beginners soon.
Keep at it!