Oh come on, no Toad Man mentions?
I beat him the very first time without taking a single hit and I was maybe 9 or 10. He's the easiest MM boss by far.
If you want the best bosses to start with per game I'll do my suggestions.
1-Bomb Man. Pretty easy level, very easy boss fight.
2-Metal Man. Pretty easy level with two E Tanks in it. Fairly easy boss fight though Bubbleman is arguably easier but getting the Metal Blade first just makes things better.
3-Top Man. Fairly easy level, really easy boss. The only problem with this is that Shadow Man has a hard stage and is a hard boss even when you have the Top Spin, so you might want to start with Magnet Man instead.
4-Toad Man. If you get hit by him I don't know what to say. Yes there is a rather tricky jump at the end of the level, but who cares.
5-Star Man. Really easy level, really easy boss.
6-Flame Man. Six is an oddball. None of them are particularly easy to go through with just the blaster but none of them are very hard either. Centaur Man is another choice if you can't get the pattern down.
7-Cloud Man. Well you only get four choices here. Burst Man is easier but fuck his level.
8-Frost Man. Very easy level (jump,jump, slide,slide.) and easy boss. Ok if you don't care about level ease or suck at the snowboard then by all means, Aqua Man.
9-Splash Woman. Easy Level, easy boss, good weapon.
10-Sheep Man. Easy level, pretty easy boss.