If you don't need to run an a/c or the microwave then by all means dispense with the generator. If you do want to use either appliance you can do that with a sub 50 lb 2kw generator. You would need an Easy Start device installed in your a/c. Works well by reducing the startup load on the compressor motor so the 2kw inverter can run it.

If you're thinking about running either the a/c or the microwave from an inverter, don't consider it. You don't have enough energy storage in your battery for that. Well possibly for the microwave but only for a few minutes at most, and you'd need about a 2kw inverter.

If you just want to run a few small electronic devices then you can use a small portable inverter or run the devices directly on 12V. For example, you can get a dual voltage TV that will automatically select 120Vac if it's available and 12Vdc if it's not. Not expensive and more efficient than the inverter option.

You can tap off a 12V supply to provide the power for either the devices or the inverter. Where you tap depends on the trailer model and where you want the 12V receptacle to be. In my 179 I tapped the supply to the stereo and ran it through the closet wall to the receptacle. The receptacle had a couple USB ports on it too.

150 watt inverter sounds like a good way to go. You just need a 12V power port somewhere to connect it to. You can get them on Amazon inexpensively. If you get one with a usb port then your phone or other device can be charged that way, more efficient than going through the inverter. You can also get them with a voltmeter which does a much better job than the crummy battery level lights.

This is an easy DIY job, you just need to find a place to tap 12V, like the power to the stereo. If you tap the main battery line be sure to add an inline fuse at that point.
15 amps for 14 gauge, 20A for 12 gauge. 14 gauge will be fine for a 150 watt inverter.

A hitch crane sounds like way too much work not to mention the additional weight. Seriously, if you do later decide you need a generator get a Honda 2.2 or equivalent and an Easy start. Easy to lift and carry around without breaking your back. That's what I used. Propane operation is also much better than gasoline if you're keeping the generator and/or the fuel in the SUV. No fumes or fuel leaks.

As for farming, you are giving me too much credit. I'm retired and we just have a small hobby farm. Other than friends and family we're not in the ag production business. Keeps us active though and we get lots of exercise. But it does ground you at home, other than a rare occasional overnight trip we can't travel, farm animals need attention every day.

  We have a Champion generator that weighs about a hundred pounds to heavy for me to lift. The generator has wheels and I use ramps to load generator up into the truck then leave ramps at home. When operating generator I roll it onto the tailgate and point the exhaust out back of truck not to fill the fiberglass cap with exhaust fumes. If I were to buy another generator I would chose a lighter weight generator one that I could lift. 

 I bought a GENMAX 3200-Watt Inverter Generator.  It is a made in China gen set but a large number of the gen sets are made in China.  It's running output is 2800 watts and so far has been able to run my AC with no easy start and it weighs 47.3 lbs which is why I bought it.  I rarely use a gen set so I figured it was worth taking a chance on and so far no issues.  I can't whole heartedly recommend it because I haven't used it enough.

Just remember that the lighter weight ones may not have the ability to start the AC reliably. You will definitely need to install a Micro-Air EasyStart on the AC in order to have a chance to get it to work. Also, on the web page, there is a bonding plug. You can build one very easily by purchasing a plug from your local big-box hardware store and connecting the ground and neutral (ground is usually green and is for the U shaped terminal and neutral which is usually a silver colored screw), leaving the brass color screw unconnected.  This is because most generators have a floating neutral. Circuit analyzers consider this a fault. Bonding the ground and neutral will satisfy the circuit analyzer.