By any you mean as low as 300 or 600mbs? USB wifi adapter w antenna?
No, definitely just the 600 mbps. That 600 mbps adapter is (almost certainly) a wireless N adapter and that (at the minimum) is the adapter that will allow you to reach that ISP speed of 70 Mbps.
I know it seems like the 300 Mbps should also easily do that to, but it won’t. That 300 Mbps-rated adapter will likely only allow you to get around 54 Mpbs download, give or take. The reason for that is largely due to wireless interference. The G standard is just more susceptible to WIFI interference than the N-standard (and later) adapters are.