The unit rating rules depend on if you're using the "Field Manual: Mercenaries" or "Interstellar Ops" rating. I have no idea about the Interstellar Ops rules, and I forget the exact Field Manual Mercenaries rules, but part of it is dependent on the proportion of high tech units you have, which is why mothballing and reactivating certain mechs will affect your rating. "IS1" is basic 3025 stuff - standard PPCs, lasers, autocannons. None of this "double heat sink", "ferro fibrous armor" and "ER PPC" stuff. If you have a mech that's got the advanced tech as part of your TO&E and you take it out and mothball it, you affect your proportion of IS2 mechs and thus your Dragoons rating.
Your TO&E affects the payment you get offered for contracts. So, before accepting a contract, you want to put every mech you've got there, otherwise you'll have contracts that pay zip.
As for contract difficulty, you need to stick close to lance weight limits. 130/200/280/380. Don't go "a little bit over", because then your employer will send your "just over medium" lance against a bunch of assault mechs. The other important thing is to keep a real close eye on enemy skill levels when taking contracts. Having learned the hard way, I will almost never accept a contract against enemy skill levels higher than regular. Had a contract against veteran opposition, and just got completely schooled each mission. Lose a mech here, lose a mech there... got lucky and the last mission was a base attack though so I auto-won when I won that, even though the contract score was like -8.
The other thing that helps is to properly manage your lance deployment. It might be tempting to deploy your lances on "scout" missions, but then you get 60% odds of a fight each week. Just deploy the minimum number of lances on scout missions, and try "defend" or "training" instead for fewer fights.
AtB also features a *lot* of tough terrain missions in crap conditions, so I tend to favor jump jets. Otherwise, you're either making PSRs for reckless movement or moving two hexes a turn.