Well, lots of advice, no surprise, many folk have fav seaside places! We've also seen many coastal locations round the UK, and though your price range will rule out a few places that got mentioned, I was surprised just now (I only tried 'OnTheMarket') to see so many possibles!
Do beware the difference between somewhere with a sea view, and plenty of boats to look at?! Worthing for example, long pebbly beach, lots of sea, not that many boats? I think Hastings would be like that too, I was never that keen.
As many have said, go north for better value, plus Scotland & Wales of course, but do research the social issues some have got. You sacrifice some winter daylight of course, and a few degrees on the temp scale?!
Anglesey looked a good suggestion, and right down the west coast (Harlech etc) to Pembroke and the the likes of Tenby and Saundersfoot. You'd have to check the exact situation re trains and boats, but lots of places in range at Tenby, for one example (huge sandy beach there too!).
Kent is good, if you can find somewhere that qualifies, though personally I DO NOT care for Margate (even in its revamped form!), and Essex is somewhere I've not seen much of, bar ancient visits to Southend (another no!).
But go somewhere like Ipswich (fairly unconsidered?), you've got boats galore, trains and properties in range.
Portsmouth and Soton have boats galore of course, (sailing, ferries and cruise ships!), and there are a few properties in range. Most of Dorset probably isn't, I saw a couple of places in Weymouth that were OK, but LOADS in nearby Portland, which you'd need to check for yourself, it's a 'Marmite' location.
ANYWHERE near Exeter is good, Exmouth has plenty houses that qualify, some over that estuary too, and Exeter is a TERRIFIC city. In N Devon, Barnstaple and Bideford are both on estuaries, loads of sailing boats and nice towns, and I think the former has trains. Houses in range too.
Jolly good luck!