i just posted on local schools in a different thread. If you are concerned about the kids learning Singlish at school, just teach them that "proper" english is to be spoken everywhere except at school (they need to fit in after all)
my kid goes to St Margaret - happy with the school.
local schools don't have a waiting list per se. there is an application process every july. Check out the ministry of education website for primary one registration.
priority of admission depends on several factors. for expats, it boils down to whether you are a PR or not (better chance when you are a PR.. altho preference for citizens). Also, church affiliations or volunteer work the year before may help, as would living within 1 km (really competitive schools), or at least within 2 km would be useful.
for schools that are in high demand, there is balloting done.
for non-PRs, they usually have to wait until later rounds...
cool thing is that some schools also have other activities for the kids eg gymnastics classes, tennis, dance, swimming... less running around for parents
do bear in mind about the "mother tongue" requirement. Usually only a choice of chinese, malay or tamil but possible to apply for other languages eg german or french but need to check with the schools directly.
other reputable schools:
1) nanyang (high pressure - jim rogers kid probably going there)
2) acs (boys)
3) mgs (girls)
4) raffles (girls?)
5) scgs (girls)
6) catholic high (boys)
7) chij (girls) - several campuses - toa payoh is good

rosyth
9) henry park (co-ed)
more out there but these are the ones i know