Here's a very partial list of rookies who both made significant contributions to their teams in 1934 and went on to have successful pro careers:
Ollie Bejma (SS, SLA) - He debuted on April 24th and will play 94 games for the Browns this year, most of which will be at shortstop. He'll play two more seasons for SLA and one for CHA before hanging up his cleats in 1939.
Zeke Bonura (1B, CHA) - The 25 year old Bonura will start at first for the White Sox and remain there until 1938 (rumors that he was interested in the owner's daughter got him traded) . Bonura was an excellent hitter, but an indifferent fielder (to put it mildly). He ended his career in 1940.
Frenchy Bordagaray (OF-CHA) - Bordagaray will play only one season for CHA, before travelling around the National League. In 1941, he'll finally settle in Brooklyn, and finish his career there in 1945.
Harlond Clift (3B, SLA) - Clift will begin his oddessey as SLA's 3rd sacker until 1943, when he'll be traded to Washington, where he'll finish his career in 1945.
Curt Davis (P-PHN) - Last year, Davis was playing on the Pacific Coast League's San Francisco Seals with a kid named Joe DiMaggio. Now, he's the ace of the Phillies staff. He'll bounce around the NL until landing in Brooklyn in 1940. He'll leave just before Jackie Robinson breaks the color barrier in 1947.
Paul Dean (P-SLN) - Dizzy's younger brother. 1934 and 1935 will be his only really good years with lots of starts. He'll see limited action and bounce around until finally hanging it up with SLA in 1943.
Augie Galan (2B-CHN) - Davis's and DiMaggio's teammate last year, Galan will play both outfield and infield with the Cubbies until 1941, with some up years and some down. In 1941, he'll move to Brooklyn through 1946. After that, he'll move around until his retirement in 1949. Perhaps the best of the class of 1934, Galan is ranked 42nd in left field by historian Bill James.
Cookie Lavagetto (2B-PIN) - Lavagetto will play about half a season with the Bucs, and remain with the team 1937, when he leaves for the Dodgers. Lavagetto is best known for his walk off double (and the Dodgers only hit) in game 4 of the 1947 World Series.
Fritz Oestermueller (P-BOA) - Oesternueller debut with the Red Sox in 1934 at the age of 26. Too old to enter WWII (34) he played throughout the war, ending his career in 1948 with the Pirates. 
Moose Solters (OF-BOS) - Solters played for the Red Sox for only two seasons, and then spent most of his 10 year career playing a few seasons here and a few there. He had a few good seasons, but was mostly a journeyman during his career. 
Tuck Stainback (OF-CHN) - Stainback also travelled extensively thoughout his career, stopping in St. Louis, Philadelphia (NL), Brooklyn and Detroit before settling down with the Yankees for the duration of WWII. He played one final season after the war for the other Philadelphia team in 1946 before retiring. Like Galan and Davis, Stainback played in the Pacific Coast League in 1933, but with Los Angelos.
