ok. so first. reputation. I didnt try to manage it. I took any mission that was available before taking the campaign missions. some liked me, some hated me...who cares, they all pay.
Re: salvage. on normal missions (non campaign) I took full salvage...and sold most of it. Only kept the ++ or +++ weapons or full mechs that moved me up. Refited mechs with the better weapons. All smaller mechs and salvage I sold. Each light mech is work 300+k, so that was my money intake. Yes there were a few times I needed to take full cash to survive, but rarely. get enough mechs and pilots to always go on a mission while others are healing/repairing. In combat, a mech I wanted, I would focus fire on the legs or head, it gives you more mech parts so you get them quicker. if you have 2/3rd of a mech, then take that last piece when salvaging to sell the full mech. who cares if you need the mech, you need the cash.
most of my Cash (non salvage) came from campaign missions. they routinely pay 1M+ if you get all the secret objectives.
Re game play. Focus fire and use precision strikes to take out one mech a turn (or two). This way you take minimal damage back and hence have your mechs available and dont have to wait/burn cash to go back out again.
Game is about limiting your damage and grabbing mechs.....