I know Propellerhead Reason does have a setting to allow other applications to use audio as well. I don't know about Ableton Live, but I found this: https://help.ableton.com/hc/en-us/articles/209770485-Disabling-exclusive-mode-for-ASIO-interfaces 

Then if you want to buy a card it's hard to give advice on that other than the many articles will tell you when you Google it. I think EMU 0404 USB is a pretty ok soundcard, but there are quite a few good brands out there, all with their pros and cons. 
What matters is ofcourse your budget, but also how many devices you want to record simultaneously do you want to be able to expand with a breakout box later, do you need MIDI, etc.