While Brian may THROW excellent thumbers, remember he is also VERY strong. That translates being able to hold the disc WELL using VERY little actual skin contact on the disc. He likes that "hook thumber" grip. You may not.
As a few others have stated here, there is NO "right" way to hold the disc when throwing a thumber. But whatever way you DO end up throwing it, it must do several things.
1. "Feel natural"
2. Allow for a clean release
3. Be on the same line as a line from your elbow to your wrist extended
4. Allow for the disc to be showing its underside to your ear at release
Eventually you WILL find a comfortable, efficient grip.
But now let's concentrate on the actual throwing motion.
Be VERY conscious of keeping your elbow (of the throwing arm) as high as possible at release. And lead with it. Think of hammering a nail in a wall about 7' up. And the edge of the disc is the business end of the hammer. If you a) don't have your elbow higher than your shoulder and b) don't warm up properly, you'll run the risk of injury, etc.
And go into things slowly. If you haven't done a LOT of overhand-type throwing (over the last year...or even in your entire life), use the "1-yr plan". Incorporate at least a dozen or so HALF-EFFORT (or less!!) overhand throws in every practice session you do for this year (yeah, I know - boring) working up to 4/5th-effort by the end of the summer, BUT by this time next year - at a minimum - you'll have 1) a "seasoned" arm for overhands and 2) will have added 50' onto whatever you're throwing now.
Ps: If you have the past 3 years of the PDGA's magazines (2 different publishers), take a look at the 2 articles in there (about overhands). Just make sure to use common sense in matching up the diagrams / pictures with the wording - as BOTH magazines butchered the articles and mis-printed the matching-up of the pic / word numbers.