You could initiate a
fraud alert (FA) for free through Transunion, Equifax and Experian (they'll try to sell you a bunch of other junk, just decline). While FA's active, any new credit applied for with your SS# will be delayed till your personal confirmation at a verifiable phone number of your choice (unconfirmed transactions should not process). When all this's sorted, you can inactivate FA for normal credit flow...
Federal law allows a free credit report annually (and/ or in cases of fraud), with free updates for a time, as corrections occur, at your request.
The best credit monitoring service I've found is
citi, which may help you watch this like a hawk. Credit insurance's generally a marketing ploy and not needed, but's included in citi's service.
Sign the back of all CC's with permanent ink; Shred your personal trash; Scrutinize convincing phone calls/ websites/ emails/ snailmail's authenticity (for spoof) if ever applying for any credit or service, online or otherwise!
Hope this helps!