In my last playthrough I took my sweet time to build a stronger lance. I bought two CN-9A
Centurion components from a store (silly, I know, but I love
Centurions and wanted to get my hands on one as quickly as I could) and salvaged a second
Shadow Hawk 2H. I then got another
Centurion component and was thus able to do the
Argo mission with two
Shadow Hawks (including the one you start with)
, a
Centurion and the starter
Vindicator (I tend to like trooper 'mechs)
. You get another
Centurion when you finish that mission and by then you have a pretty nice little lance available, with the
Vindicator and
Blackjack in reserve. By that point I'd sold both the
Spider and the
Locust to keep my company going through hard times, but with a solid medium lance and ever-improving pilots you should be able to take 2-skull missions without too many issues. If you need a recon 'mech, I suggest using the Firestarter and dropping the flamers and MGs for 2 more MLs and armour.
At this point you can start thinking about doing Assassination missions
@Jade_Rook mentioned - one of these netted me my first heavy, a
Catapult. After that salvaging becomes easier - prioritise salvage over C-bills and you'll make your living off of repaired 'mechs, keeping the best ones for yourself.
Once you get the
Argo your 'mech refits will progress far quicker, so you have more opportunities to change your loadouts. Based on personal experience I'd recommend outfitting a
Centurion with an AC/5 (w/ two tonnes of ammo), 2 MLs, 1 SRM-6 (w/ one tonne of ammo) 4 JJs and 3 HS. That leaves you with 10,5 tonnes for armour, which is
very solid for a starter tank build. You can capitalise on that by giving its pilot Bulwark once you reach Guts 5.
By the time I got to the second storyline mission I had a TDR-5SE
Thunderbolt as well as the
Catapult and mediums mentioned above. I sailed through with no issues. Do note that every single one of my 'mechs has JJs on - this allows you to make full use of the varied terrain in BT.
Further down the line I'd consider hiring and diversifying your MechWarriors to the extent that you can field two fully self-sufficient lances with mutually-supporting skillsets. Assuming 10 MechWarriors (including your character) I'd go for 4 Vanguards (Master Tactician really comes into its own in the latter half of the campaign), 2 Outriders (my favourite build for recon pilots who don't need Sensor Lock), 2 Lancers (your go-to assault 'mech pilots) as well as a Gladiator (best used with heat-intensive 'mechs or when you absolutely, positively
have to fire off one more Alpha strike) and a Scout. You could also consider getting a Skirmisher or a Flanker, though I prefer the former because of the way Multi-Target and Breaching shot synergise. Have a look
here to go through all the pilot builds.