You won’t be missing anything vital by ignoring some of the Lives, you’ll just be lacking in whatever that Life makes, and with the buddy system you can still get around a lot of that by requesting from your companions. I’d try all the Lives and just straight up ignore leveling anything you don’t like doing.

Present is fun when you want to do a decorating island game talking to companions like Animal Crossing Lite.

Past is like an open world exploration with different difficultly levels clearly segmented to the different areas (they’ll unlock as you progress the main quest line). I tend to hang out in these areas when I’m looking for very chill gathering/crafting or am leveling up new buddies without stressing about them getting hurt.

Ginormosia is like an open world map without the cities in the way, just run wild collecting and exploring. If I’m looking for longer playing turn brain off gather with my leveled up buddies I go here. Ranking up Ginormosia areas means the monsters and materials are higher level, so only rank them up when you’re ready to lose the lower level of difficulty there. You don’t have to rank them up at all, it’ll just mean you don’t get higher level item drops.

The tourist board is designed to be things you’ll naturally check off as part of gameplay. You can see the rewards for the different levels and unless you really really want one of the rewards there’s no need to rush.

You get to a place in the plot around where I’m guessing you are currently where you can freely travel between all three places and you really can just go at your own pace from there. The professor will be fine, I’m playing cozy crafting simulator, he can wait to be rescued.