Over the several years you have researched, things have changed. In particular price of lithium batteries.
If you have grid-tie net metering available, and if the terms don't change (remaining 100% credit for backfeed), DIY GT PV could pay for itself in 2 years and give free electricity for the following 18 years. Inverter life of at least 10, maybe 20 years should be expected, and is maybe 20% of cost, can be replaced economically. Panels should be delivering 80% to 95% of initial power after 20 years, should last 40 years. But some models degrade, some quite rapidly; it can depend on environmental conditions also panel design/material problems.
Not relying on net metering, low-cost batteries should be cost effective. (High cost batteries are same price per kWh of cycle life as the grid so worthless for saving money.)
A battery inverter running 24/7 rather than just when the sun shines could have lifespan half of a GT PV inverter. I don't have first-hand knowledge of that. SMA warrants Sunny Island battery inverters for 10 years, Sunny Boy PV inverters for 20 years. I ran 5 Sunny Boy for 17 years with a couple failures, calculated about 32 years MTBF.
Because PV panels have become so cheap, 10% of what they were couple decades ago, maybe 5% for second hand, an alternative to battery may be to greatly over-panel, use-it-or-lose-it. Cheaper to make more electricity at $0.025/kWh than to sometimes buy from grid for $0.25 to $0.50, or to store in batteries costing $0.05/kWh or more.
To answer your initial question,
As a general rule, what would be the first component that I should target installing? I'm thinking that would be a grid-tied inverter and an emergency shut-off switch but I wanted to get some feed back.
Grid tied inverter automatically shuts off when grid is down, UL-1741. A separate switch is suggested by the utility (maybe required in some jurisdictions) so they can positively isolate it, otherwise could pull meter leaving you with no power.
If you start with a basic grid-tied inverter, that won't grow into a system with backup, except by adding a separate battery inverter. If you go that route, plan and price the future system. Enphase microinverters may work best with Enphase battery inverter. Most string inverters that support Rule-21 frequency-watts should AC couple with grid-forming battery inverters like SMA Sunny Island, Outback, Schneider. Newer Enphase have difficulty with that. Sunny Island may be discontinued?
For more money up front but less money overall, you could use a batteries-optional hybrid. That's why I mentioned SolArk earlier - people here who have it generally seem satisfied.
Likewise, is there a guide laying out what order components should be installed in? My thinking is that once that is in, I can work on the solar array as time/money is available and connect it to the inverter which would already be in place. Likewise I could add a battery array as finances allow and keep doing that until I've reach my goal.
Plan and price in advance. Batteries can be the most expensive part. Currently, 48V LiFePO4 server-rack batteries seem to be the best price, but several may be needed to supply starting surge for motors. Some systems have no communication battery <--> inverter, those that do require specific models (which may not continue to be available.)
I've already been researching and planning this for several years. Your assumption is that I haven't. I know the design of my system but wanted input on what to install first. Again, I respectfully disagree that my electric bill won't go down over time and that I wouldn't have electricity when the grid is down. I appreciate the feedback though.
Please tell us the models you are planning to use. Features and performance vary, and people here have experience with many.
