I'm amazed nobody has mentioned the best resource available for anyone new to classical music: the radio!
BBC Radio 3 is broadcast in the UK and also streamed to the world at 320 Kbps AAC which sounds really nice. As well as play back of CDs and discussion and interviews and features there are live concerts every day, usually two! These are not just collections of jobbing musicians knocking out some toonz, these are usually performers of the highest calibre. It's amazing. Radio 3 gets some deserved criticism for its morning shows which have dumbed down so we have to hear about how Doris of Basingstoke felt moved to tweet her deep appreciation of Bach while walking the dogs this morning and other similar inanities, but the music is still good and if you don't switch on until lunchtime you're spared the social media bs and interviews with weather show presenters and minor celebs.
It's on the BBCs iOS and Android apps, and iTunes, and plain old www pages. And if you just want a playlist url you can use the same one that iTunes does: http://www.bbc.co.uk/radio/listen/live/r3_aaclca.pls
Also very good is
Concertzender a Dutch online broadcaster. Their pages are also available in English (mostly) and they have dedicated streams for Classical and Early music and even for sub-genres and other types of music. They also broadcast live performances.
The Czech Republic has http://www.rozhlas.cz/portal/portal/ which streams in high quality ogg vorbis.
Anyway there are numerous online stations out there and a few like those above offer really high quality streams and comprehensive published schedules and/or metadata so if you hear something you can find out exactly what it is. This is a brilliant way to discover music, and about history, context and the people.
The other resource that might be much better than you think is your local independent classical music shop, if it still exists. I live somewhere with a population of about a quarter of a million and there is now just one such shop left. It's quite small but has a good selection of new CDs and SACDs and two other great features: there is always some music playing and there are thousands of used CDs at great prices. Used CDs are cheap! I've found brilliant CDs that cost me pennies. Lots of them. OK I've bought a few that should never have been made and some that are fine but not to my taste but that's part of discovery and it's still rewarding. And while browsing I've heard music I've really enjoyed and been able to buy it right there. I might never have known that Respighi's unfinished Violin Concerto even existed let alone had been lovingly completed and brilliantly recorded, but I was browsing the used stacks wondering what this music was that I'd never heard before. Shortly afterwards I have in my hand the CD booklet to read while we listen. Then I buy it. It's a nice type of human experience that isn't duplicated by an online store.
