I use the slip at New Brighton on the other side of the Mersey. There's an annual permit required but it's a lot cheaper than it's listed as. I think the council website says something like £120 but if you pay at the RYA school there then you can join their sailing club for £30 and get the permit for 50-odd quid a year. You've got a fiver a day for the tunnel too if you're going from the Liverpool side.
You can launch at most tide states except high water springs (so the leaflet says, I've never tried). It does mean driving out on to the sands if you're launching at low tide but they're reasonably solid, the jetskiers drive out in Astras and Honda Civics. It's OK if you can keep out the water as the tide cuts the sand from under you, I saw a guy in a 4x4 van badly stuck a couple of weeks ago. I usually push the trailer in by hand and tow it out on a rope, keep the car on the dry. There's a tractor as well, I'm told it's about £15 each way. Parking is free.
You also get the use of slips at Dove Point and West Kirby. The one at Dove Point is restricted to 2hrs either side of high tide, the other one is tidal too but never been so don't know much about it.