There are a few important factors to consider when choosing interfacing.
The first is if you need woven, non-woven or knit interfacing. Non-woven interfacing does not have a grain and is suitable for most interfacing needs. Woven interfacing does have a grain, much like fabric, and the interfacing should be cut the same way the fabric was (on the bias, on the lengthwise grain, etc.). Knit interfacing has a bit of a stretch and is suitable for interfacing knit fabrics.
The next factor is the weight of the interfacing. Interfacing comes in three weights: light weight, medium weight and heavyweight. The weight of the interfacing should be equal to, or a bit lighter than, the fabric.
If you do get interfacing on your iron (something I’ve done more times than I’m willing to admit), unplug your iron and let it cool. You should be able to peel off most of the interfacing. This is time-consuming and annoying. You can use a solution like Goo Gone to get rid of any sticky residue.
Some sewists recommend adding a second press cloth underneath the fabric, just in case. This protects your ironing board cover, in the event that the fabric and interfacing shifts.