There's a café now on a farm, about 100 yards from the Mickle Trafford end of the Millenium path. I think you could park there (if wanted) before doing the ride, it's cycle friendly. Sadly, and stupidly, there is no other parking at that end of the path, but there is further down a bit.
It's a great ride with various options, depending how far you want to go. I usually go to Shotton, then cross over the road by the blue bridge, come down the path by the river Dee, as Neil said.You can then come back through Chester (I can probably knock a map up if wanted) then you have further options again about how to get to Mickle Trafford. We usually do the above, then the A51 out of Chester, left into Barrow, follow through to the A56 then back to Mickle Trafford.
It's tarmac all the way so road bikes are fine to use, as are (of course) hybrids and mountain bikes. There are a lot of dog walkers on there, especially between Hoole Bank and Blacon, so just keep your wits about you, as some of them are off the lead and wander all over the place. We always keep our on the lead by the way!
Also watch out for a tiny minority of racers who go flat out and never give warnings of approach, and there is now speed bumps in at Blacon. The wind usually blows you back from Shotton to Chester by the way, so starting at Mickle Trafford makes things a b it easier if you want a gentle run out.