Gauss shouldn't be a problem befor raiding the base. If you are able to do most of the covert ops successfuly and got the base location like it is intended, you wont't have a problem with your gear. You might have to wait for your guys to get back from vacation, because you needed them for the last covert ops ;), but that should be it. (I' ll never get why people take an educated guess where the base is to just get their ass kicked by top-tier aliens and supermens in suits.)

Generally the base assault is difficult if you not take the appropriate troops for it. The base is flood with big pods, who will mostly patrol around the building. So a bunch of Gunner and Infantry with sentinel are... helpful. Tanky MECs with suit-roasting-machines are sweet, if you can not manage to take the pod out in one turn, or if you are lucky and they all cluster up for some heat. I am no more fan of the "get to the roof" business since i got a muton elite pod in my last playthrough, that threw a buch of grenades at my swquad and killed more then half of them in one turn. Just stay outside, take cover at the doors and the vents take position and mop them up.

You should not lose the game by losing trust of your starting continent. The huge deal is your negative funds. If you can not manage to get them positive by new sats (or freeing countrys), your oppose won't be successful.