HSV1 is most commonly transmitted orally, and is commonly called "cold sores".
HSV2 is more commonly transmitted genitally and is the one people think of as herpes. However, you can have HSV1 genitally as well, and some people have gotten oral HSV2.
Generally as long as you don't rub virus in your eye or give birth during an active phase (they do C-sections to reduce the transmission risk then), neither of them are particularly horrible except for the immunocompromised.
Yes, they stay in your system, but so does herpes zoster (aka chickenpox), reappearing as shingles.