This is a huge area and personal preference is going to drive the choices to a great degree. For a good answer some parameters need to be defined:
Are you only going to operate the rig if you are in trouble?
This defines the size/cost/weight of your choice. If you are going to also operate “normally”, the rig can take up more of your space/weight budget. If you intend to only operate in emergencies, then something small and light is probably best.
What mode will you be using?
CW, SSB, or both?
Define travel. Are you going to be on foot, horseback, dog sled, snowmobile or other motorized transport?
Obviously this makes a huge impact in the weight and size categories. Anything other than on foot realistically opens you up to just about any portable transceiver. On foot, then something small with small (light) batteries is appropriate. But the size there depends on how far you are going and if you will operate at other times than an emergency.
Who would you be trying to reach: other preppers, State Troopers, Alaska National Guard SAR, USCG, Mom and Dad? How far away are these people and what are the conditions (propagation-wise, in general) you will face where you are going?
This would define the capabilities needed in your rig. Your cute ¼W 40m CW only Tuna Tin II won’t do you much good for contacting the State Troopers, for example.
I don’t have a “go bag”, I live on the coastal plain between Baltimore and DC and there’s no hope to escape the region for a sudden event. And if it’s not sudden, I have time to pack and being an organized individual, I could probably still get out of the house faster than many with prepared plans. If I did live away from large cities with only 1 or 2 roads out of the area, my bag would look like this:
1) My Android Smart phone with spare batteries. This has the usual assortment of apps loaded including a repeater listing app that only requires your GPS fix, not a connection to the network, to function. Gives you bearing and range all repeaters in 25/50 miles depending on the setting.
2) SPOT Personal Tracker -- 99USD MSRP. This is a GPS / Satellite unit that you can use to check in as OK or to summon help. Uses commercial satellites to route “911” calls to the nearest SAR outfit to your location. They make larger units that also function as regular GPS devices. I wouldn’t hike outside of cell coverage without this or something similar, emergency conditions or not.
3) Cheap Chinese 2m/440MHz HT. I have a couple. These are small, light and so cheap and useful, even if you have a nice HT, having a few of these around is handy and at $35 each they are some of the cheapest ham gear you could own.
4) Small folding Yagi for 2m and/or 440MHz. These weigh almost nothing when made from an old tape measure and take up no room. With one of these, the Chinese HT and the repeater book off the phone, the chances of hitting a repeater just went up dramatically.
After that it would depend on answers to the above questions.
For me the answer is my FT-817. It’s hard to beat the DC to daylight coverage including the 5MHz Alaska Emergency Frequency. For casual use or emergency only use, the internal batteries are all you need. I have the W4RT NiMH pack in mine and it lasts me for hours. If I want more time, I have a pair of NiMH packs from RC planes that I have set up with power poles. Together the 3 packs last me 15-20 hours. It has an internal keyer, so add a set of travel paddles, a 20m dipole and a VHF/UHF dummy load, I mean rubber duckie and I am set.
I can use the dipole on 40m and 10m with acceptable SWR in a pinch. If we are talking non-foot travel, then adding a tuner would be good. Perhaps other antennas, my BuddiPole/MFJ vertical has given me contacts out to a couple thousand km at 5W. the whole thing packs up to about 70cm long and 1-2kg.
YMMV, but here's a start.