Yes it was made largely by the OG team of Black Isle, currently working in Obsidian. New Vegas was pretty much a loose sequel to the original games, as it took place in Nevada, which is on the west coast, just like the originals (F1 in California, F2 in Oregon), hence all the deserts, familiar faces, familiar themes, factions etc. Fallout 3 and 4 play out on the east coast, far away from the events of NV and originals, the only major reference I can remember is Harold in Fallout 3.
They are amazing RPGs, really grim yet humorous in the best possible way.
My favorite is Fallout 1. Fallout 2 had more features and it was "bigger and better" in general, but I kinda prefered the main theme and the ending of Fallout 1 more. Chill, no spoilers. I dunno, going out to look for water for the vault spoke more to me than being some savage tribe-man looking for a magical garden-making device. Fallout 1 felt more desperate and grounded for me, and that's pretty much the only reason I prefer it over 2.
My gripe with New Vegas is the very underwhelming "Wild, Wild Wasteland" perk and being very buggy, but hey, that's Bethesda engine for ya.
As for Tactics... I hated it, gave up on it after like three missions. It didn't work for me, not one bit. Not really an RPG, AI was very weird at the time, and it was very frustrating, as it's real time tactical game. I don't feel like I missed out on anything worthwhile.