A B737 CREW; DEPARTING BDL; OVERSHOT ASSIGNED ALT AND EXCEEDED 250 KTS BELOW 10000 FT.

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I AM A NEW LOW TIME IN TYPE FO. I WAS FLYING MY FIRST LEG OF THE DAY. OUR TKOF INSTRUCTIONS WERE SIGNIFICANT (TURB AND WINDSHEAR IN THE CLB TKOF 20 KTS). WHILE CLBING OUT I WAS VERY FOCUSED ON THE SIGNIFICANT AIRSPD CHANGES (40 KT RANGE) TRYING TO MAINTAIN A SAFE CLB PROFILE AND CLEANING UP THE ACFT. APCHING 3000 FT I ATTEMPTED TO ENGAGE THE AUTOPLT; BUT IT WOULD NOT ENGAGE IN THE DESIRED MODE. I MADE A COUPLE OF ATTEMPTS THEN DECIDED TO HAND-FLY; MADE THE 1000 FT TO GO CALLOUT. WHILE I WAS TRYING TO STABILIZE AIRSPD AND BEGIN LEVELING OFF; APCH GAVE US A TURN. I REACHED UP TO TURN THE HEADING BUG AND BEGAN THE TURN. AT ABOUT THE SAME TIME THE CAPT CALLED OUT 'THERE'S 4000 FT' HE QUICKLY LOWERED THE NOSE AND PULLED THE THROTTLES BACK AS WE BALLOONED TO ABOUT 4500 FT AND MOMENTARILY EXCEEDED 250 KTS. I THEN CONTINUED TO FLY AS PER DEP'S INSTRUCTIONS. DEP MADE NO COMMENT AS TO OUR EXCURSION FROM ALT. IN RETROSPECT; I SHOULD HAVE FOCUSED ON LEVELING OFF BEFORE STARTING THE TURN SINCE THEY WERE SO CLOSE IN TIMING AND I WAS SATURATED; OR ASKED THE CAPT TO SLEW THE HEADING BUG WHILE I FOCUSED ON FLYING THE TURN AND LEVELING. I HAVE ALSO LEARNED THAT TRYING TO ENGAGE THE AUTOPLT AT SUCH A BUSY TIME CAN ACTUALLY ADD TO THE PF'S WORKLOAD AND BE DISTRACTING AND A HIGHER WORKLOAD THAN HAND-FLYING. SUPPLEMENTAL INFO FROM ACN 535362: IT WAS THE FO'S LEG; AND AFTER TKOF FROM RWY 33 WE WERE CLRED TO FLY RWY HEADING TO 4000 FT. IT WAS A VERY WINDY NIGHT AND WE ENCOUNTERED MODERATE TURB ON THE CLBOUT. THE FO WAS HAVING TROUBLE WITH THE FLT DIRECTOR AND HE DECIDED TO DISCONNECT THE AUTOPLT. HE WAS RAPIDLY APCHING 4000 FT AND I POINTED THIS OUT. HE STARTED TO MAKE CORRECTIONS; BUT I TOOK THE ACFT AND PULLED THE THROTTLES TO IDLE AND DSNDED BACK TO 4000 FT. THE HIGHEST WE GOT WAS 4500 FT. I SHOULD HAVE BEEN MUCH MORE VIGILANT AND SHOULD HAVE TAKEN THE ACFT SOONER ESPECIALLY AFTER HE DISCONNECTED THE AUTOPLT.