Recommendation for small cutter

Engraving bit size (~1/32d), but for cutting on hardwoods. I’ve ordered the engraving set from the store here. But I still have it in my mind that I might need something heavy-duty. My project is for very small jewelry pieces around 1x1x.25". I’d like to cut at least 1" thick stock with it.

If you’ve got something in mind, I’d appreciate it if you would be verbose about the “why.” (I’m new to machining in general.)

Thanks in advance!

I bought one of these with several spare inserts. At the moment, this appears to be the last VBit I’ll ever buy. I use it on very hard hardwoods, plastic and stone. Still using the first cutter insert after 6 months. Be aware that the postage can be horrendous if like me you’re ordering “internationally”.

http://www.toolstoday.com/p-6015-in-tech-series-insert-v-groove-router-bit.aspx