I haven't done a comic yet, but I've done stickers and t-shirts.
The first one was pretty hard because I was new to it, but it helped me gain a few followers on Kickstarter. The next 2 went very smoothly and I gained a few more followers on Kickstarter.
I promoted mine mainly through social media, Instagram where I have the largest following, and on facebook.
I did a little paid advertising on facebook, and Project Wonderful, but not much. maybe $25 total.
I wouldn't worry about coming across as needy, or annoying. Maybe post it once every few days. If people get annoyed with you, then they don't need to be following you anyway. Just let everyone know what you're doing and why you're doing it.