In order to get the data I needed I used the custom leaderboard feature over at Fangraphs. I based my rankings on a couple factors including the amount of games they played in March/April, and wRC+. I also used some other statistics, and included them in the spreadsheets so that you can make your own conclusions.
T10) Justin Morneau
Justin Morneau was on his way to another MVP season, posting 206 wRC+, and did it in 21 games. He had 21 non-intentional walks, and only 2 intentional walks. That success continued throughout the season, until he sustained a devastating concussion in the summer. Morneau has struggled to be the same ever since.
T10) Robinson Cano
Robinson Cano didn't have as many walks as Morneau, but he struck out less than he did. He also showed a little more power than Morneau did. Cano maintained the hot bat all year, and finished with a 6.5 WAR.
9) Evan Longoria
After having an incredible 2008 rookie year, Evan Longoria posted some excellent numbers in the first month of his first full season. He showed that the power was real, and that he had an above average eye at the plate. There isn't much else to say, he's a stud.
8) Alex Rodriguez
Alex Rodriguez would be up higher, but he did it in 27 games. The K% was a little high, but it eventually regressed. Rodriguez preceded to finish 2003 with one of the best seasons of his career.
7) Chase Utley
Like Rodriguez, Chase Utley is also lower because he played in 28 games during March/April. He didn't disappoint though, managing an excellent strikeout and walk rate, while showing his power potential.
6) Alex Rodriguez
While Alex Rodriguez's 2003 start was good, his 2007 start was even better. He showed mammoth power, posting an ISO of .527. The strikeouts also weren't as concerning as in 2003. A typical Alex Rodriguez start.
5) Brian Roberts
In 2005 Baltimore Oriole's second baseman, Brian Roberts, had a career year. His power in the first month of the season was a fluke, as was his power throughout the whole season. In the end he had 6.7 WAR.
4) Albert Pujols
Just a typical Albert Pujols start, he showed a ton of power, while hardly striking out at all. There isn't much else to say.
3) Jose Bautista
It's funny how fast people forget things. Just last season Jose Bautista was the hottest player in baseball. In 24 games hehad a 255 wRC+, and showed off incredible power. He ended the season as one of the best players in baseball.
2) Barry Bonds
This could arguably be the best April ever, Fangraphs writer Dave Cameron certainly thinks so. Bonds had an uncanny ISO, and got walked 45% of the time, 18 of his walks were intentional. It might not get any better then that.
1) Matt Kemp
With all of that said, I think Matt Kemp has had the best start in the past 10 seasons. Bonds showed much more power, and Kemp came second in wRC+ only to him, but once you reach 200 in terms of wRC+, things become less clear.
There's no clear cut answer, all of these guys had incredible starts to the season. Some of the players had better starts were better than others, but in the end they all were dominant.