I'm in agreement with ipe, but thought it was worth noting that the price for premanufactured ipe thresholds is currently 5 times that of oak. Oak is also good quality and often used for outside door jabs. Oak has a long history of surviving punishment. Although, if you build your own threshold you could save a lot that expense. Other notable woods are maple and cherry, which some people find prettier, but you need to make sure it is well sealed or else you'll probably get some unsightly water stains.
Extending or building the threshold depends somewhat on what (style) you buy. Premanufactured thresholds are pretty self explanitory and some come with harware (screws). If you are looking for custom build ideas, I think you could try studying the designs that already exist.
Grocery list: knee pads, sawzall, hammer and prybar (to remove old stuff?), borate for termites, subsill and toe kick, flashing (over the subsill and top edge of the toekick), adhesive, skill saw, jigsaw, and/or coping saw (for shaping and/or cutting the horn), medium grit sand paper, screws and drill, foam filler, caulk or silicone caulk blend, paint or varnish.