Here are my 2 suggested orders for defeating the Robot Masters:

Method 1:

Galaxy Man
Jewel Man
Plug Man
Tornado Man
Magma Man
Hornet Man
Splash Woman
Concrete Man

Method 2:

Splash Woman
Concrete Man
Galaxy Man
Jewel Man
Plug Man
Tornado Man
Magma Man
Hornet Man

I prefer Method 1 as you get Hornet Man's weapon sooner which can help get items, but both Galaxy Man and Splash Woman are easy with just the Mega Buster

A few Miniboss tips:

The Dragon on Magma Man's stage can be killed quickly with Galaxy Man's weapon, and it has the added bonus of sucking up the fireballs that will damage you.

In The Rockslide section of Jewel Man's stage, watch the stones at the top when the Stone with the face rolls back up there, it will show you where he is coming out next.

Dr. Wiley Bosses:

Level 1:

Maga Man's weapon can make things easier, but the mega buster works fine.

Level 2:

Part 1:
I found the Mega Buster to work well

Part 2:
Tornado Man's weapon makes short work of this section

Part 3:
Splash Woman's Weapon is powerful here.

Level 3:
Galaxy Man's Weapon is good against this boss.

More as I get there.

Wiley Mode 1:

Use the Mega Buster to bounce the eggs back in the Robot's mouth.

Mode 2:

Use Cement Man's Attack

Mode 3:

Plug man's is the most powerful but you will only be able to hit it when it flies in low.  Other than that, Hornet man's attack is a good way to hit him when he is far away.

One last tip:

On Dr. Wiley Stage 1, there is a section with 3 horizontal magma man level beams that is quite tricky. The way I got passed it was to equip Rush Jet then climb the ladder to that section.

Immediately jump on top on the bottom most beam, then immediately fire a rush jet to the right. Jump on and right it up to the rightmost ladder.

I found that in Wily Fortress, level 2, part 3 of the boss, Galaxy Man weapon is very useful too because it will absorb the lasers.