If you want to try a BM, you want an Axis if at all possible. And for $5-$10 more than a mini-Grip you can get a full size Grip if you'd rather have a 3.5" blade and hand-filling knife than a sub 3" that's easier to carry.
If I *had* to recommend a BM under $40, I'd say get a mini-Ambush. A hell of a lot of knife for the money, much better than the Pika and I prefer it to the Monochrome.
Once you've made the jump to the axis, knives above the Grips get pretty subjective. I don't have a single bad word to say about the 710 or 805/806, but a lot of my love goes to the insanely ergonomic and tough-tipped 730/732/735, and in small-but-built the 705 has a fanatical following. (And I just ebayed a nominally used one for $46.) For an axis that cuts big and carries small, the 940, 943, and 921 are all world-beaters, if you like aluminum handles.
On the cheap end - for the same price as a Grip you can get a 530, an axis folding boot/dagger pattern. Very flat, v-e-e--r-r-r-r-y light, excellent cutter. But it's so light that it feels flimsy, and many people prefer Grips for their stiffer, tougher feel. I'd recommend a 530 unreservedly for performance, but based on popular feeling I'm not as sure you'd love the feel of it the way you will a Grip.
The BM I carry most is my 770 GRN/BLK, but all the 770 series are quite expensive. The BM I take when I know I need to *use* a knife is my 730. My 730 is why I no longer own a 551 Griptillian - I liked the Grip, but the only thing it has over the 730 is a lower replacement cost.