you won't get much 'mech for ten million. It's hard to get decent VEHICLE forces for that budget.
I suggest focusing on motorized squads and platoons, maybe some mechanized units, but focus on two things:
1. distribution
2. bang for your buck.
you need to be able to spread out and emplace, and you need the maximum kill for the Hbill.
to that end, analyze your city, determine the places an enemy 'mech or vehicle will want to go, and mine the everloving crap out of those areas, concentrate on concentric rings of preplanned demo, mine fields, and traps-places your platoon or squad can cross, that will collapse under (and trap) a combat vehicle or battlemech.
iow, yes, you want combat engineers to go with your dakka.
but my advice is next to useless, I'll almost always endorse lots of light infantry when your immediate C-bills aren't conducive to a better alternative.