OK, I'll try and keep it shortish. Not something I'm too good at...
The Netherlands is a fantastic place to live, I'm sure you'll love it!
Leiden is a great little city. Oegstgeest, it's main suburb on the Amsterdam side, is also worth a look. Another bonus of Leiden is that it's only 20 minutes from the sea I've not lived in Amsterdam so can't really comment on it's suburbs. Sorry.
School starts at age 4 here but my DC are both under two so it's not something I know too much about. Finding a Montessori school shouldn't be a problem though, there's even one in our village! Nurseries are very widely used here (maternity leave is only 10-12 weeks) and there are usually waiting lists at the better ones. The standard is generally pretty high though.
Playgroups are pretty thin on the ground, although I'm sure there will be some if you're living in a city. There are none in my village and it's not a small village by any stretch of the imagination. There is an English language toddler group once a week in Voorhout, a village about 10 minutes outside Leiden.
The public transport here is great (but the Dutch complain about it constantly) and cheaper than in the UK. You can get an idea of prices here. But, road travel can be a total PITA at peak times. Commuting between Leiden and Amsterdam by car would mean often sitting traffic jams unless your DP's working unusual hours.
Not speaking Dutch isn't likely to be a problem at all, almost all Futch people speak good English. It is worth learning a bit of though, well, as much as possible really. It makes things much easier. The DC will almost certainly pick it up really quickly
Are you looking to rent? This site is very widely used to advertise properties.
Plaats of postcode = Place or postcode
Prijsklasse - van/tot = price class - from/to
Zoeken = Search
Erm, ok, I think that was all the things you asked. Hope it's some use! I must go to bed now, will check back tomorrow.