You didn't mention your load requirements for the shop, but since you mentioned just running a 120v line OK you said 110 but almost all normal home voltage in the US is 120/240 So I'll call it 120v. In general most 120v circuits in a home are limited to 20 amps there are some instances where a dedicated circuit may be 30 and even 40 amps, these are rare for most homes.
However a 40 amp 120v comes to 4800 watts (VxA+=W) with that in mind a 20 AMP circuit at max can draw 2400 watts
Now talking about generators the optimum generator size depends on the total continuous load the minimum size of a generator should be calculated to be using no more than 85% of total start up wattage output. Things like air compressors air conditioners refrigerators just about anything with a motor will have a significantly higher start up current requirement than the run current. There are ways to reduce these high start up currents by using capacitors and delay start relays tricking the motor into believing it is receiving double or even triple the amount of current that it is actually drawing from the power source, but that is a subject better left to A friend of mine in New Zeeland
After a long round about route to your question Solar versus propane generator/ versus a trench for a line to the shop. Or just dragging a heavy duty extension cord out when ever you need power in your shop area.
Long term if you never planned on moving then burying a line would be the way to go Dig a trench and bury a non metallic conduit and fish the conductors through it.
There are trenchless ways to bury the conduit as well either horizontal boring or vibrating-plow which feeds the conduit through by only making a thin deep cut, no soil is removed to have to be back filled. The advantage of pulling the conductors through a conduit is they are not exposed to the soil conditions and you can up grade later on should your power requirements increase.
Solar has its merits but the up front costs can be staggering
A portable generator fueled by propane will almost always be labeled duel fuel meaning you could run it on gasoline if you are out of propane. If you do a search you might even find them on sale after hurricane season as surplus over stock just the other day I saw a new 12,000 watt duel fuel generator on Ebay for 499.00 a unit of that size could power your whole house in a power outage and with the proper transfer switch gear if the power went out it could start up and run in and be powering your house in about 1 to 2 minutes.
For my money if I had any thoughts of ever moving the shop the generator would be the way to go but also have a 100 lb propane tank as the main fuel sourse with a bbq grill sized tank for back up