Tinkers are the class of choice for people who want to either make use of as many shops in the dungeon as possible, or to farm up gold in between "serious" runs. They get the most mileage after the player has done several runs through the bonus dungeons, since their wallet will be larger and the plentiful shops will begin stocking rarer items.
Because of this, the build for a tinker is largely defined by what the shops have in stock. If you get lucky, you could have an invincible death bringer who fears nothing. Shops are almost always useful in the long run, though, so you're unlikely to be screwed into a poor character.
Race and Deity Choices
Tinkers are the one class for which the Goblin race is a solid tactical choice (assuming you tend to gather up gold in between serious runs), since they can toss glyphs to get that last bit of cash for a neat item. (As of v0.2, this is no longer true) If you're uninterested in that, you should probably stick with human or dwarf to play the odds and ensure a useful all-around character.
The really interesting choice for a tinker is Tikki Tooki. Since it costs gold to join up, you need to ensure that you'll come out ahead if you gain the Gold boon, which isn't a very sure thing, so Tikki Tooki is probably to be disregarded. The other gods' utility is as defined by the shops as the rest of the tinker's playstyle.
Almost all races are useful for this dungeon, and as usual with the Tinker, it really boils down to whether or not you get good items and Glyphs. It really helps to try this later on, when you have lots of shops and high-level items available (though even lots of mid-level items can do you good).
Try to find BURNDAYRAZ early, and begin taking out the highest-level Animated Armour you can be fireballing them repeatedly. The exploration you undertake while doing this would hopefully reveal many shops with useful items, and/or The Pactmaker, whom you should try to join early on. The key is to level up as quickly as possible, keeping low-level (4/5 and below) Golems and Meat Men unharmed as much as possible.
Once you reach level 7, set up a a level-up with the highest-level Golems and Meat Men remaining (since at this point killing Animated Armor will be more wasteful in terms of explored tiles). Engage Iron Man and take him out using Glyphs (especially useful are HALPMEH and CYDSTEPP, as normal for this dungeon). Level-up halfway, and if necessary use up a few potions and/or a shop item, but try to reserve resources for Super Meat Man.
After Iron Man is down, set up another midfight level-up. Your remaining resources should suffice to take it out. Again, you really need to find a combat Glyph other than BURNDAYRAZ for this.
Another strategy, which is much easier but is only possible if you have APHEELSIK, is to first attack Super Meat Men, at level seven. Keep hitting, poisoning, and then exploring untill he is dead or you run out of tiles to explore. If you are lucky, you should be able to kill him without having to do a midfight levelup, and killing him will level you to level 8. At this point, convert APHEELSIK, as it is useless against the Iron Man. Iron Man should now be very easy as you can set up multiple midfight levelups.