jonnylocks

I would second that suggestion, Lithium battery. Specifically I would recommend a LiFePO4, LFP, battery. They have the safest chemistry out of the common Lithium battery types, light and reasonably high energy density. One other advantage to LFP batteries is the terminal voltage. At full charge they are around 13.3 or so VDC, a very good match to most mobile equipment that expects 13.8 VDC. The battery has a very flat voltage verses discharge curve so when the terminal voltage drops to 12.8 VDC the battery is almost completely discharged, like around 80 to 90 percent of the rated capacity is used. Don't try this with a lead acid battery.
 
I've also found they have a very low self discharge rate. You can charge them up and let them sit for months and the terminal voltage hardly drops. For an Ecom application this would be an advantage.
 
I've wreck enough Gel-Cell lead-acid batteries over the years I won't buy them anymore if the equipment can use the LFP type. Lead acid batteries don't like sitting around unless they have a trickle charger attached and don't let them sit around at less than full change, they will sulfate the plates. Neither of these conditions hurt LFP batteries. As a matter of fact one recommendation for long term storage of LFP batteries is to discharge them to around 50-80 percent of capacity, they can stay that way for months to a year or more this way without damage.
 
While LFP batteries are much more expensive than the common lead acid type once you ruin a few lead acid batteries you'll get sick of replacing them and the cost adds up.
 
I've had good luck with the following company for LFP batteries.
 
https://www.bioennopower.com/collections/12v-series-lifepo4-batteries
 
If you want to use a solar panel to recharge the battery a small MPPT controller designed specifically for LFP batteries is required. I have several from this company.
 
https://sunforgellc.com/genasun/
 
I have a couple of the GV5 charge controllers, a good match for a 50 watt solar panel.
 
For solar panels I got some from this company.
 
https://www.renogy.com/products/solar-panels/
 
I have a couple of their 50 watt mono and 1 of their 30 watt mono panels. The build quality is good and they do guarantee them.
 
On solar panels from my experience don't expect to get more than around 70 to 75 percent of the panel rating, which is derived under lab conditions, which you won't get in the field.

I don't have any specific recommendations.  I don't operate QRP, though some of my friends and fellow club members do.  I have been out in the mountains with them while operating and it it amazing to see how well they get their stuff to work.  I would recommend finding a group or forum the specializes in QRP.  That would be a much better resource of information.
 
I suggested 40 meter because most people can/will only have one device.  40 meter is global comms day or night, while compared to other bands, such as 20 that works best during the day and possibly not at all at night... or 80m which works the best at night, but possibly not at all during the day.  You can get much better efficiency and a smaller antenna with 20m, but you risk not having night time comms.

Richard made a great recommendation above with the Sat phone.  That is really the best bet for coms.  I didn't think of it because it is very expensive and requires you to have an account.  I default to HF radio because that's what I do, its cheap and doesn't require paying for an ongoing service. But, if you have the funds... Sat coms is likely the best solution.
 
 
The Amateur Radio community considers anything 150 watts and down to be low power.  Saying you have or should use a low power radio can be misleading due to that.  QRP is Ham lingo that is typically used to abbreviate the point that you are using low power to communicate, but typically 5 watts or less.
 
An affordable example of a radio would be a XIEGU G1M HF radio.  Also, kits are available from companies like QRP Labs.
 
You can make your own end-fed wire antenna for a couple of dollars.  Or a dipole.  There are a ton of video tutorials on YouTube that show you how.
 
For a battery... a small 12.5v lithium ion or gel cell should be fine.  they are between 50%-60% lighter than lead acid batteries.  The lighter the better.

The basic premise here and the bulleted proposals above ring true for me - that there needs to be better and more centralized support for beginners. I have multiple college degrees and technical knowledge but the practical advice (such as what the OP cited) is scattered across the internet. For an old technology with such potential and use, this makes no sense to me. 
 
Great comments all around though and the replies above are well taken.