I've heard that it can be helpful to host on an established domain (like blogger) and gain some of their trust which can help you in the SERPs. Does anyone have any experience in this? Does it help, and if so what are some good sites for it?

It's not worth it if you intend to blog for any significant amount of time. What you might want to consider is purchasing an expiring domain from a drop catcher or an already-owned domain from whoever owns it.