Does a solar company do some sort of evaluation of one's specific home/lot/roof to see if you get enough sun to make it worthwhile
This is certainly possible (and not terribly difficult) with some basic solar-calculator software, and good companies will do this for you. At a minimum, they should be calculating the average solar irradiance for your specific neighborhood for each month, and then incorporating your roof exposure (compass direction), roof pitch, and any obstructions (e.g. trees, other buildings). Software makes this easy now, so there's little excuse for not doing it.
A good company should show you exactly how many kwH of electricity you can expect for each calendar month for your specific roof for a given sized array.
How to tell if they are actually doing said calculations vs just pulling some average number out of ChatGPT? Here's a few softball questions to ask: If I removed [Specific Tree] - how much more electricity will I generate in December? In June? What is the calculated monthly energy (e.g. in kWh/m2). If they can't give you specific values, or if their estimates on how removing a tree in Dec vs June are linear ("it goes up by 10%!") They don't know what they are doing. Ask them to show you their calulations/software.
I can I trust that evaluation even though it comes from someone trying to sell me something?
Great, you are aware they are salesmen trying to sell you something! Surprising how many people don't get that dynamic. First, you should get multiple quotes from different companies, and ask each for the solar energy on *your* roof on a monthly basis. They should be similar, though not exact (it is modeling afterall, and inputs matter). If they diverge, find out why.
Second, get references, and ask them how closely their installer's model matched their actual solar output. Solar installs come with fun little features to track energy over time, and people **really** notice when their system underperforms. Just ask "hey, how many kWh did [Solar Company] say you'd likely generate, and how much did you actually generate last year? Over the course of 1 year, estimates should be within 15%.
Finally, ask the installer if they provide a "Solar Guarantee" for performance. Some will promise a token amount (usually the rate your utility pays) for underperformance. Usually it's a percentage, starting around 90% and dropping to 80% after a few years. Warning, it sounds better than it actually is, as your system has to underperform substantially and then you're generally entitled to the difference, which may only be a few dollars a month *if* you bother to file a claim.
I'm at about 39*N latitude.
Your latitude matters far less than your heating/cooling needs, especially at 39ºN. Even more important is whether you have net metering. You will generate a lot of electricity in April - July, and very little in November - February. Your roof angle, exposure and surrounding trees matter less during the summer because of the high sun angle. It matters a great deal for winter-time production. I'm a bit further northan than you, but I frequently break 30 kWh on sunny days in June but struggle to hit 10 kWh in January on even the best days (3-4 is more the norm). I simply can't heat my house in the winter on solar and rely on net metering to keep my bill at $0 (plus grid-tie fees).
it would be nice to be at least partially solar and have the system as a back-up if power goes out. (I'd likely do a battery.) And to help push our energy usage more to off-peak hours, too.
Be aware that most solar installations cannot power your home during a blackout unless there is a battery backup. It's a safety feature so that PV systems aren't sending power back into the grid, potentially injuring line workers or arcing through downed power lines. Further, your battery configuration will determine whether you draw from the battery vs the grid at night (or during rainy/cloudy days with high usage). Some configurations will not allow you to recharge your batteries from the solar panels if the grid is down, which means your battery backup may only a night or so.
But I don't want to buy an expensive system if it doesn't get enough sun to generate much energy.
What qualifies as "expensive" is quite subjective. Almost always, air sealing and improving insulation in your home will have a much bigger impact on energy use than installing solar, until you've done all the easy bits. There's also a value on having an automatic backup power system (in the case of a solar-tied battery) which works silently, even if you are not home, and the value of renewable energy. Those factors might be worth $20k to you, or $20. On the other side - there's a lot of embodied energy in battery backup systems, so batteries take you in the opposite direction if your goal is to get near carbon neutral.
If your main goal is just to have emergency backup power for occasional (few times/year) blackouts, a gas generator with transfer switch is the most economical choice if you are confident you'll be home during the outage. An auto-on, whole-house generator can be installed for about the same as what a battery backup will cost, and provide you with way more power (albeit by burning a lot of fuel inefficiently).