You're pretty much spot on with what you'll need for a really detailed campaign.
Strategic Operations will give you enough for the advanced rules dealing with support staff and repairs.
Tech Manual and Tactical Operations can help out with the equipment and costs.
Total Warfare for standard game play with 'Mech and non 'Mech forces on the table.
Campaign Operations gives rules for how to create a Merc group with an established reputation and all the fun "history" that would come from a bunch of sellswords. Also the book has rules for generating contracts as well as how to build actual bases.
You've already got the A Time of War so that's going to be redundant if I talk about it.
For an alternative, abstract, campaign I'd suggest:
Any of the pdfs that use Chaos Campaign tracks. In fact there's a Succession Wars one for free on the site. You lose the "nuts and bolts" of paying for specific weapons and wages for support staff though. You pay some flat Warchest points, boom it is a repaired 'Mech. Now you just go out there and fight.
Also recommended in this abstract version of campaigning: Alpha Strike. Basically the Battleforce stats with a range that's a compromise between Total Warfare and Battleforce. Fights are quicker but also deadlier, but you can house rule that "dead" and dead are subject to a die roll for all the players know.
At the time of this post, I can't find a good replacement for Campaign Operation in terms of making contracts in any abstract way. So CO might be good to serve as an inspiration of sorts.
Recommendations if you really want to go all out nuts:
Interstellar Operations is the "way out there" book I enjoy because it lists era and availability of stuff from everywhere.
That could be a fun GM toolbox to spring stuff like "Oh hey this mumblemumble Pirate faction, somehow snagged old prototype stuff that's almost lostech" sure your players might be surprised, but then only to find out this stuff is bulkier and has mods against its roll compared to the more "streamlined" stuff they know. Still those would be fun shake ups here and there.
That's why I love this game. Pick and choose what fits the scale of your game and the time you have available.
Plus yes MegaMek's loving crew of fan nerds does have the HQ program. I've used it here and there, solid stuff. I'll let the others' praise speak for that.
Thanks everyone!! I remember that about contracts the Field Manual: Mercenaries had very detailed rules for that, apart from rules to create the merc unit, but as none of my players have played Battletech/Mechwarrior before I wanted to keep things easy to begin with, so the rules on Campaign Operations seemed the appropiate resource. Also I will be managing most of the crunching of the unit, at least for a few sessions, so no need give myself more work :P
I know its an older resource, but I really like some of the stuff in mercs handbook 3055
especially some of the supply (standard supply kits) refit and upgrade materials etc.
I think one of the books I mentioned (don't remember which one right now) also has the rules for refit kits (which I hope the campaign will advance enough to be able to use them.
By the way we have already done one training session so they get used to the tabletop game and their mechs, and will have the second one this weekend, so we will be able to begin the campaign proper pretty soon.
So far the unit is composed of a Awesome 8T, Orion, Archer, Shadow Hawk, plus the technicians and a Leopard. I would have prefered them to use mediums to begin with, but they wanted heavy metal.