crimson
I don't really go for Classic FM, just snippets of pieces. Try BBC Radio 3, they've gone down the Classic FM route at breakfast time which I think is a shame, but the rest of the time you do get whole works. Keep an eye on their "Composer of the Week" and sooner or later you see one come up you fancy. Then there's a programme of their music, with good commentary between the tracks.
Also listen out for their live concerts, in the evening or afternoon. I'm sure many people on here will agree there is something special about listening to a live concert, sometimes with roughnesses, rather than polished and perfect recordings. Is there any sort of classical music festival near you. Can be very good.
Visit a few local charity shops and buy a few CDs. Usually 50P or £1 each so mistakes aren't expensive. Buy 3 or 4 composers you like the idea of (perhaps from the lists above) and see how you get on!
Is there a CD library near you? I found that a great way to get into classical music. You will probably find the music librarian very helpful.
Then the one biggest help I found is the Rough Guide to Classical Music. I cannot recommend it too highly. Some brief biographical details on each composer, then some careful thoughts on preferred recordings to buy.
Hope to buy recordings. Not easy. If you have a local record shop, try them, they will be delighted to help you (probably). Otherwise I use www.amazon.co.uk.
Do you want to buy CDs or downloads. You can often buy second hand CDs in Amazon. Should be very cheap.
Don't order from their American site www.amazon.com but it has clips of most purchasable music. Which will usually enable you to decide if you like it or not.