Easy to go and stay long term. You can find accommodation by asking around, especially taxi drivers - notices in supermarket windows, shacks etc. Expect to pay around 10,000 rps per month (about £125) and do not pay it all at once - just say you have a pension which is paid monthly and that is how you will pay the rent. You can stay in BB accommodation for about 600rps ( £7.50) per night and pay nightly but this is more expensive than paying monthly but you can move around, staying in different areas until you find something you really like.
As for Brits - the place is full of them - on the beach - in the bars and restaurants etc. both holiday makers and "long stayers"

it must be easy jonny- we have at least one member who went out for a holiday the best part of a year ago and hasn't been seen since

Would that be our Lezlie Fiona hes gone very quiet

Thanks Narial,
i fancy starting of in candolim for a couple of months and then going south, if i like it i will probably do this every year. My mid life crisis is kicking in and if i dont do it now i never will.

Been doing this for about 12 years - you will find plenty of accommodation that time of year. South Goa completely different to the North - much quieter but still people to chat to etc. Depends what kind of place you are looking for - Candolim beach area is quieter than Baga and Calangute but still plenty of beach shacks - just more spread out.