You will not 'lose' your Internet but you should check with your provider to verify the cost of web-only options.
And you do not need an "HDTV" antenna -- any conventional TV antenna will work just dandy. Even 'rabbit ears' ...
True, there is no such thing as an HDTV antenna, but rabbit ears... only if you live very close to the tv station.
@OP: I suggest you check out antennaweb
to see what size/type of an antenna you need.