Thanks for the opinions Tim!
After many hours, variations, tweaks, i have come up with a final 2 logos, based from the first ones in my original post. Each one has 3 variations, which is making me hard to choose from!
1a; from the original post, removed "graphic" and altered the descender.
2a; changed the M to more of a slab serif.
3a; extended the slab serif across the top
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2a; mixed the ideas together, using the m from the first idea, and the g from the second.
2b; a custom m, made from circles, this matches the contours of the G better, and has a constant width, like the G does.
2c; slab serif on the M.
I do like the first idea now, but still unsure whether a logo with "design" is professional enough. As Tim said, i have a website, business cards etc to show i am a designer. Also with the fact i do photography and web design / development alongside graphic design could cause some confusion.
Any ideas opinions towards these ones?