Doomsday is one scary SOB if he's played right.  Right off the bat he can be a jungler or a capable laner.  I'm normally a ADC player and i came across a DD playing with this similar build and tried it our for myself (with my tweaks), its highly effective.  Of course against a strong power user, you'll want to be careful, but here are some suggestions i have for the DD noobs

1) you'll want to get comfortable to Lane as a melee.  If you're a ranged type of guy like me, getting used to standing beside someone to poke them.  Last hit, last hit , last hit... when you can 

2) you'll want to get comfortable to Jungle.  your kit allows you stomp on jungle creeps and minon waves easily (especially after your ulti).  

3) Learn how to use your goddamn "E".  Your teammates will thank you.. I've played enough where a novice doomsday will carry a 'reachable' enemy champ , out of range and let the champ get away.  Learn to time your "E" and position them that you are either pulling the champ into your allies or into a wall (wall hits give them a minor stun). Arguably it can be used to pull an enemy champ away that is killing a friendly champ, but, bottomline is just to use it.  

Starting Items are simple, get your cloak and health vials.  Because DD doesn't have energy or will. 

Core items, make sure you level up lobos for that early boost, but getting your Suit of Sorrows depends on how well you are doing.  The key is that Suit of Sorrows has reflect and so does DD's ulti so you want to capitalize on that.  

All the other items are situational, if you are the only one capable to jungle you might want to start with maurader shield first and then work your way up.  Otherwise focus on ADC items (Joe Chills, Deathstroke's claymore) or sustain items (Soultaker Katana).  Which if you are farmed up enough , can make you a scary som-a-b!tch in the mid-to-late game.. if not and you are behind you might want to focus on defense to help cover your allies and setup ganks with "E".  

An interesting idea by DocteurV is to use Ruby + Spear of destiny.  Which is a great idea as well.  Capitalizing on DD's already high health early on with Spear's ability to use a percentage of max health as damage is a double-whammy.  My only issues with Katana and Ruby are that they are highly dependent on coin boosts (which aren't a problem to get, but rather to keep).  However if you are tanky enough, no need to worry about that. Also the Skill order would vary too given this variation, since the passive does give you bonus health you might want to consider upping this even before "W".  (assuming you get your Spear Early, which would be the key).

Stolen powers, i like to get invulnerability for jungles and early tanking, but can substitute for consume if you're going to jungle.  Super Speed is great for setting up "E" by running ahead of someone you can set them up for hitting a wall or back into your allies. for the kill.  or if its one hit, just stick a fist up their wahoo. 

For skills 
R > Q > W > E > Passive

Your passive kind of sucks, but you definitely don't need to upgrade "E" either, focus on "Q" because it gives you a minor stun on the third one, and "W" helps on creep-wave/jungle clears.  

1) Jungle - for extra cash when not laning, 
2)  Setup Ganks - use your "E" well, 
3) Stomp/kill/rage!!!! - the rest is auto attack

More to come as i experiment more