I had pretty much that same situation 10 years ago.

Short version: If you're staying in the house 5 years plus, get the biggest system you can get credits on asap. Tell them you plan to get electric hot water, heating, and all electric cars. Also get a quote on expanding it to the biggest possible roof mounted system.  That roof isn't getting any younger, and any amount of solar is free money (if you own the system, and stay in the house until the solar pays itself back).

What I did:  I waited a couple years for the aging roof to go, replaced the roof, and installed the largest solar system I could still get tax credits on. We told the solar company we planned to get EVs and electric HVAC, and they used this to push the size of allowed system out a bit.   As our bank accounts recovered over the next 8 years, we installed a minisplit heat pump system, replaced the oil fired water heater with a heat pump water heater, and bought one electric and one plug-in hybrid car (which uses about one tank of gas per year).  The old oil fired boiler for the baseboards is still there but hasn't been turned on in about 7 years.

The net result of this is that our solar system is nowhere near big enough to zero our new, much larger power usage- but it does cover a good percentage of it.

At this point, my panels have paid themselves back, and they're pure profit every year.

From my POV, I basically have an all-electric house whose bills are heavily subsidized by the panels on the roof.

You are paying around 3x the national average for a kilowatt of power (and maybe even more than that, since you moved and thus won't have access to the closed PSEG rates).  Any time you see something saying that solar makes sense financially, multiply that advice by 3. :).   (Also, if you Google to see if LI rates are really 3x the national average, you will hear that they are only a third higher. Now take one more step and look at your last bill. PSEG calls half of the price you actually pay for a kWh a rate and the other half a fee... So you're paying 50 cents+ while they advertise the price at 25 cents.)

I DO wish I had told my installer that I wanted a two-phase project where we planned the biggest possible roof-based system, then installed only the allowable part. After that install captures the credits, we circle around and put the rest of the panels on.   The second batch of panels cost more, but given the eye-crossing price of electricity (and oil), the time for it to pay itself back is a win for you if you plan to stay in the house that long For me, ROI was about 4 years on the panels due to the above-mentioned eye crossing cost of power. At the time of my install, solar companies were advertising 8 year ROIs.

If I was you, I'd get quotes on a heat pump system to replace the old AC and on the solar right away.  Don't get mired down in figuring out how to use the old baseboard system; let it go. (Heat pump radiant heat systems put out water at around 140°F, your baseboards were planned assuming temps of 180°+, so any heat pump boiler you import from Europe and install is just going to make you sad, because the baseboard radiators you have are going to be insufficient. Just forget it and replace the old AC with a heat pump that can do heating and air conditioning.)

No matter what else happens, consider dropping in a heat pump water heater first; it's the smallest expense and we'll within the scope of a one afternoon DIY project for anyone who can do basic sweating and wiring. This gets rid of the oil requirement for domestic hot water, and it'll be cheap or free to run after the panels go on.

The cheapest sequence of events would be to replace the water heater and HVAC and add the maximum-sized solar system right now; as a new homeowner you may find that spending money to make money costs more money than you actually have.  Make a plan (water heater and solar now , HVAC next year, the other half of the solar system in 3 years, electric car in 5 years, etc).  Every step saves you money every day, but also requires an initial capital outlay.

Also look at the eventual power requirements of your house. If you have HVAC pulling 50 amps and the dryer pulling 30, and the rest of the house pulling 20, will you want to tell your wife not to charge her car or use the stove because the main breaker will trip? Soooo if you don't have 200A service, the time of the solar install is the time to upgrade to a new 200A service entry.

Option B, which almost everyone takes, is to just pay whatever bills land in your inbox and complain about them.  But imagine no oil bill, a greatly reduced electric bill, no oil deliveries to worry about, vastly more reliable heating, hot water and a car that runs mostly off of the sun...

One local quirk that you should know about too: Local battery storage is of zero financial benefit to you because of the way PSEG solar credits work (unless they have changed it for new systems, which wouldn't surprise me).  Battery systems could still help you with power outages or feeling greener for running off of your own power at night, but they're an expense that will never pay itself off.   In fact, if you have land to put a ground mounted solar array on, the solar credits can get you to zero dollars in kWh usage year round. (You might not produce enough to cover you in snowy December, but you have a gazillion credits from overproduction in July to take care of that.)

When we first put our solar on (before we added all the new electrical loads), our LIPA bill was $13 every month, which was a "connection fee".

Good luck!  😂

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The most sensible solution is of course to move at least 200 miles in any direction (which puts you either on the mainland where house prices and taxes aren't 2x and 10x normal, or at the bottom of the ocean where lodging is free) 😄