There are good and bad HHs. Aptasia anemones are probably the most common form or the latter along with majano anemones. Various types of algae (bryopsis, etc.) can also be difficult once introduced. Good HHs' would be sponges, corals, worms (although some can be bad), pods, etc.
Honestly, I don't think a 100% dry rock cycle will take all that much longer than a tank with some or all live rock. The only way to speed things up is to buy 100% cured rock and keep it wet until you get it in your tank. The concern with some dry rock is that it is not clean. BRS pukani rock for example is beautiful rock but it is loaded with dead sponges and other organics which are burrowed deep into the rock. This can lead to an extended PO4/nitrate issue. A bleach + muratic acid bath will take care of that. The BRS reef saver rock, Marco's and Reef Cleaners dry rock is pretty clean. If you are looking for ease, buy the cleanest dry rock you can find and simply add an ammonia source.
Much of the dry/base rock i see locally is very clean but it is also very dense. There appear to be pores in the rock but they are only surficial. Basically the rock is heavier than it looks. If that is the case with your LFS rock, you may still want to buy online. If it looks like the stuff on marco's/BRS website, then go for it.
No damsels or any fish for cycle. A table shrimp or pure ammonia will do the same thing.