This is the plan I followed a few months ago and was successful in starting up a Tiger that had sat for 29 years. There are many ways to skin this cat (pun intended…) My suggestion is to read a number of responses and make a plan that you are comfortable with. The following is what worked for me so take it for what it’s worth…
1) Cooling system. Drain it. Remove the fan belt and give the water pump a spin by hand. Personally, I look at a WP as a wear and tear part that generally doesn’t like a long sit and one that can leave you stranded or worse, so cheap insurance to replace.
Thermostat - like the WP, just replace it. It can give you huge problems if it gives up at an inopportune time.
Hoses - I wouldn’t trust them…
I think you are ok to test run an engine for two minutes with no cooling system just to see if it runs.
After you have the first successful engine run, go back and get the cooling system squared away. Consider removing the radiator and having it pressure tested. Replace all heater hose lines. Look into how to pressure test your heater core and heater valve. Inspect the engine block freeze plugs for signs for leakage.
2) Fuel system. For an initial run, plan on rebuilding the carb before you even try to start it the first time. Yes, it may be just fine but diaphragms for the accelerator pump and power valve have a large tendency to dry out and crack over time. Plus, you want to have a first hand look at your float and needle valve. I got a gasket kit from Mike’s Carburetor (no affiliation) for $25. I cleaned all the passages and replaced all the diaphragms ( mine were all shot). In addition to correct performance, a carb that has been gone through will mitigate the chances for an engine fire. How foolish would you feel to have your prize kitty-car go up in smoke?
Fuel pump - remove it and test it out of the car. That way, if something bad happens you don’t have a fire hazard on the same level. I’m not familiar with the stock pump, so look for more advice on servicing the stock pump.
Fuel line / filter - replace the rubber hoses and filters between the fuel pump and carb. If you have a stock car, be sure to replace the small section of hose that connects two section of tubing that is located right next to the starter. Replace the filter, don’t trust an old one.
With the fuel line section disconnected between the fuel pump and the carb, careful spray in a generous amount of carb cleaner and let it soak. After a day or two, carefully blow out the line with compressed air. If the line is more or less clear, run some construction twine through it to swab out the line. The easiest way to accomplish this (take it away MacGyver…) is to get a small funnel, some duct tape, and a shop vac. At the carb end of the fuel hose that is next to the dipstick, insert a small plastic funnel. Target has a good kit for just a few bucks. Attach the funnel to the vac line with the duct tape. Determine how much nylon construction twine is reasonable to get from one end of this section of the fuel line to the other. Power up the shop vac and after checking for leaks near the funnel, offer the construction twine at the fuel pump end of the fuel line. It may take a little fiddling, but eventually you will be able to get twine through the whole section of fuel line. Once the twine is successfully though the other end, pull the twine back and forth a number of time to loosen up and debris that might be lodged in the line.
With the fuel system closed between the fuel pump and the carb, temporarily install a few feet of fuel hose immediately before the fuel pump. Get a small plastic bottle (half a liter to a liter is good) to use as a fuel source. This quantity will give you about a 3 minute run time.
As many have mentioned, ALWAYS have a fire extinguisher at the ready when you go for start up the first time.
3) Oil system. Change the oil and filter. Look for any obvious compromises to the oil filter hoses. When you drain the oil, look for any signs or chunks of sludge. If there are any indications of sludge or substantial debris of any kind, plan on dropping the oil pan. It can be done with the engine in the car. With the pan down, you can clean the pan and the oil screen completely.
With fresh oil and a new filter, remove the distributor as many have suggested. Counter clockwise rotation is required on your SLOW turning drill. There is a small hex drive between the cam drive gear and the oil pump. There is a specialty tool for this, but I used a long 1/4” drive extension and a small socket. I taped the socket to the extension so the socket didn’t come off. Slowly drive the oil pump - you will hear it when it starts pumping. The oil pressure gauge is mechanical so no electrical power is required to observe a pressure reading. Let it run at full speed on the low setting on your electric drill for 20-30 seconds. Look again at your oil filter hoses for leaks.
4) Electrical system. Set up the minimum for an initial run. Plan on running the starter, fuel pump, and ignition system off the battery. Spend some time inspecting your electrical connections at the fuse block next to the voltage regulator. A few jumpers and some version of a remote start switch are pretty easy to configure so that you can be running the starter while fiddeling with the throttle. Yes you can just leave everything plugged in and use the key if you are confident it will work and want to start the car from the cockpit not in the engine compartment.
5) Cylinder treatment. This is important and requires patience. The objective is to get oil on and around the cylinder rings to prevent binding or a stuck ring. The dangers of a stuck ring are many but a gouged cylinder or poor compression are the chief hazards in my opinion. There are a number of ways to go on this. Fogging oil, ATF, Seafoam, but my favorite is Marvel Mystery Oil. Many have used this product on antique aircraft for many years with much success. Pick the product you like but the procedure should be the same. Essentially I recommend dribbling 2 ounces of fluid into the cylinder via the spark plug hole using that small funnel you used earlier and a small piece of hose when the piston is at bottom dead center before the compression stroke. Pull your distributor cap and all spark plugs. Pull the engine through several times with a 1/2” drive ratchet and a deep well socket on the crank pulley bolt. 90º of crankshaft rotation or two spark plug positions before the ignition point on the distributor for the corresponding cylinder should be BDC. Confirm this with a plastic straw used as a feeler to see when the piston is at BDC. After applying the appropriate quantity of oil in the cylinder, reinstall the spark plug. Then move to the next firing position and repeat the procedure for the next cylinder in the firing order. When pulling through to the next firing position, pull slowly. The idea is that the oil will compress into the compression and scraper rings as well as thoroughly coating the cylinder walls. With all cylinders treated, let the engine sit for a few weeks. The longer the better. I did this step first. It took me a month to complete the other steps so the rings had ample time to soak in the oil.
Don’t get in a hurry. Be sure to have an observer/fire guard present when you go for a start attempt.
Good luck! -Kevin