Frame- Your frame is what connects all of your parts together, so this is a very important part of your bike. A good frame and fork are made out of 4130 cro-moly, but beware frames made out of hi-ten are worthless if you plan on doing any serious dirt jumping. Different bike companys use different frame geometry and top tube lengths, finding a frame that suites your needs will make it easier and more comfortable to dirt jump and ride.
Wheel setup- You want a strong 48 spoked (or 36 if you are a smooth styled rider) but if your like me you'll need a 48 spoked wheelset. For axle size I would sugest 14mm axles over 3/8 because even tho bein quite a bit heavier than 3/8 the 14 mm can take alot more abuse. If your going with any high end hubs they should be using sealed bearings, if not consider a different hub, because with dirt jumping your rear hub gets exposed to alot of dust and grime. Cleaning sealed bearing hubs- Just whipe off any dirt or grime off the shield and lubricate with Finish line Teflon Lube to keep them running smooth. If you want have a good setup get a Casette rear hub which will be more expensive than the conventinal hub/freewheel setup but will run smoother because the rear gear will be sealed unlike normal freewheels. But if you want your wheelset extra strong and reliable, have your wheels handbuilt at a bike shop. They will be able to get required spoke tension, wheel alingment (no wobles) and corect adjustments to perfect running condition.
Handlebar, seat hight, and chain tension- Handlebar widths very from rider to rider, most serious riders cut there bars down as much as they can. Small width bars make barspins, x-ups or any bar tricks easier. My bars are cut down to 24" width but with bar ends on its 25" wide, which is a nice width. The angle the bars are posisioned also very from rider to rider. Every rider ahs there own personal feel. I run my bars to the same angle as the fork. This provides for comfortable riding for me. Seat hight should be set to where you can easily pinch your seat with your knees in the air. Stand on your bike and try to pinch the seat, and adjust it according to your needs. Chain tension can idealy be set up to where the chain is very tight, making it so you have no pedal float (spining of the crank while your feet are off in the air) making it easier to land no footed tricks. You can get your chain tight by tightening your chain tensioners tight.
Tire setup- Tire setup can very depending on what kind of surface your riding on. New trails with paths and jumps will probally benifit from having both front and back knobby tires because of the good grip they provide. Differing from that situation, developed trails may benifit from riding knobby in front and freestyle in rear. Because the ground is hardpacked like concrete, aslong as you keep the dust and rocks off of the path a freestyle rear (or possiblely front too) tire will be able to grip better than a knobby. So depending on your riding surfaces your tire setup may differ, find a setup you like and keep with that. Tire presure should always be at or above what is recremended, If below you may get pinch flats if you come up short and case the landing. But idealy I run my presure to around 60-70 psi which alows me to keep speed up. But if you case the landing with high presure tires, you may not be able to just ride away from it you may crash or hurt your wrists or ankles.
Cranks and brakes- For dirt jumping you will need a strong crank. A 3-piece crank is a good strong crank. Profile makes a good line of 3-piece cranks, don't just go and buy a cheap brand or a 1 or 2 piece crank because you will just end up waisting your money on it and end up going to a repetable crank company after. For stopping you need some good u-brakes. Dia-compe makes a good u-brake there 996 or 990 brakes will get the job done right. For barspin and other moves you may want to get a gyro. But if not you can just run your brake cable long so you can spin your handlebars without hang-up or harming your cable. And any platform peadals with replaceable pins will give you grip to your shoe.
Conclusion- When starting out dirtjumping you will be hard on your bike, theres no way around it. When you damage or break a part when replacing it replace it with something bettre, because if you replace it with the same as before it will just end up failing on you again. And you'll be able to have a better jumping experience if you have a good strong running bike to not have to worry about.