Both of them were great! Kintama arc shows the charismatic side of Gintoki and how his friends care about him while Ikkoku Keisei arc tells us more about Shouyo sensei and of course, for people like you who ship Gintoki x Tsuki.
Oh, I am currently watching the whole series at the proper sequence. I really liked Gintama after post episode 10, so I guessed I am lucky in the sense that I actually liked it early on and need not to go straight into the the more-serious arcs like most people do, and I actually have time since I have a 6 month break from school C:
Yep, Vacation Arc is from Gintama', it starts after the Renho arc and before the scandal arc, after the scandal arc its Baragaki arc.
The arcs that you missed are funny arcs, however, I didn't really liked the Correspondence arc.
I might pick up LH sometime, but not so soon though, as I've too many things I want to watch now.
My strategy when it came to Gintama was pretty darn weird. :p I was short on time due to school and exams so I went ahead and watched most of the 'action-heavy' arcs first. I only completed the original series this year. But I still think I missed an arc or two. Also, Enchousen had those awesome arcs back-to-back (third wasn't as good but mehh) so it was a great watch.
I do plan to rewatch the whole series, this time following the proper sequence.