As well as budget, figure in what school system is going to suit you best as well as length of the commute (if you are going to need to do it). Kent is a grammar county - only 25% of kids pass the 11+ and on the offchance your children don’t, if you plan to go State you don’t want to end up in an area with a poor Secondary school of which we have many.
I know Folkestone is becoming increasingly popular but with apologies to those who are keen, it doesn’t really float my boat. Deal is nice and popular and is attracting a lot of inter Kent and London arrivals and has some very well priced period properties. Broadstairs is also attractive.
Whistable and Rye are gorgeous & historic towns and I’d happily live in both. £600K would get you something really nice. On the downside, the State Secondary in Rye is poor and the commute from both into London (with a change in Hastings) is really long and not really do-able on a daily basis.
While it’s not on the coast, Battle in East Sussex is on a direct line into London and is a really pretty town with a good community feel and a very rated Secondary - Claverham. It’s only a short drive to the coast from Battle. Hastings old town with its winding streets is nice as are the houses around Alexandra Park. Hastings has a very mixed demographic with problems with drugs and homelessness but there are ‘good areas’. The Secondary schools are not good though. People do do the commute to London but it’s a long journey! Bexhill is better on the school front and while it’s reputation is that it’s a retirement town, it’s increasingly popular with young families and has nice properties and a good beach as well as regular arts exhibitions. The train journey with a change in Hastings to London would be un-doable on a daily basis.
Living on the coast is really great in the summertime but can be grey, unpleasant and freezing cold battling along seafronts in the wind in winter! Sorry that’s a bit negative!