I would definitely always prioritize registering and locking in your place for your home regional. It's always nice to show up there every year and be a consistent and familiar team. It actually kinda helps with alliance selection if you have a good reputation. I know my team has been picked before for eliminations, even though we didn't do that well. Because we're always at the Sacramento regional, we can get picked since we have a fairly good reputation. But we always hope to be the ones picking, and if not, we want to be picked for our scouted merits, not just for being there every season.
My team generally does two or three regionals a season. On average, it's two. Our budget was in a big deficit after the 2013 season since we went to three regionals, won two of them, thus ending up at champs, for a total of four events in a season, with champs being the huge expense. I wouldn't recommend jumping to three regionals in a season anytime soon until your team knows that they either have enough, or can make it up in sponsorships and fundraising post-season. But two regionals is a good area to get comfortable first with having more than one chance at a win.
I am excited for your team's progress and initiation into the fictional "two regional club!"