How hands off vs hands on do you tend to be when investing? What drives how involved you become?

Curious to hear from angels, VCs, etc here — how do you decide how much involvement to have with a founder or startup after investing?

Do you prefer staying out of the way unless asked? Or do you take a more active role (e.g. strategy, intros, recruiting help)? What factors make you lean one way or another — founder experience, check size, stage, your own bandwidth, etc?

Would love to hear some real-world experiences, especially if your level of involvement has changed over time. I recently launched my own thing last week and we've gotten a fair amount of attention but a little apprehensive to raise funds with a perceived bias that the strings that come with a cheque may not always be in the best interest of the end user.