does it matter to you if the mechs have paint schemes from different regiments or even factions?
See, I was thinking I would split my mechs into companies, 1 per House and paint them up as a prominent Regiment, and then some additional mercenary lances. But, without mixing mechs between Regiments, that severely restricts the choice of which mechs can be used at one time. I only have one Wolverine so if I paint it Gray Death, I still want to be able to pick it when running something else.
No, it totally completely, fully does NOT matter.
Your plan is a good one, its one I started many years ago (you know, when I get around to painting every 6-months to 2-years).
I refuse to own 12 Locusts just so every house & merc can have one. (The 7 I own are too many & I need to downsize to maybe 4 for a perfect lance, lol)
My personal suggestion is to do what I did.
1. Look at your entire collection & select out all the "house specific" or at least "heavily favored" mechs. And put them into that house.
IE. So the Dragons, Panther, Jenners, & such went to the Draconis Combine.
The Enforcers, Valkyries, Jagers, & at least 1 Warhammer/Rifleman went to the Fed Suns. My lone MenShen will be MAC (CC) for sure. Etc etc.
2. Then, once you have your basic force, say 5/12 for the company?
Fill in based on mechs that are at least "common/produced" by said faction. So the FWL got a Wolverine & Quickdraw to go with their earlier Hermes-II, Orion, Awesome.
The Kell Hounds got a Wolf Hound. Lyrans got a Griffin. This should fill in at least 3/4 of your force or so I'd think.
3. Finally, take your super common &/or multiple copies mechs & use them to fill in the last few slots. (Like those 7 Locusts I mentioned or my 7 Guillotines which went around to 7 different regiments across several houses/factions).
4. In conclusion, no, you don't have to field anything that matches at all, you don't even have to paint them, but many people like to so they are all purty like.
Arrayed out, they can look nice when they are pattern matched into Lances/Companies, etc etc, but once it's time to battle on the tabletop, its all about making a force by BV & not by Paint Scheme. The Davion Guards goes into Battle right along side the Ryuken & the Marik Militia.