Depends on your intended use. Communicating with other hams you know may require a whole different setup than communicating with other hams randomly.
...I assume any modern set will be able to connect to a laptop and send packets
Anything that has an audio jack can be used with just about anything with a soundcard or audio capability.
...Does SDR allow for the same hardware to do HF plus other bands?
This question is difficult to answer without further info but generally SDR stands for software defined radio which is superior, in my opinion of course, to older technology radios. It can be used to span 'DC to daylight' frequencies but, as with everything else, capability comes with a price.
Check into APRS radio for short text messaging needs that offers global coverage and is built into some very inexpensive VHF radios. Packet communication is slow but with APRS it's not really an issue.
Thanks, so much to learn. :)