So… I have this car now and I want to give it the old college try 
First, I need to replace the tires. Bonus is that the two front tires are super flat. What should I do? Buy spares and then take it to a tire place? What kind of spares should I buy? Or… how else should I go about this.
Any jack recommendations? Any tips/tricks I need to know when changing the tires?
Thank you!!!
Before anyone else chimes in.
Welcome.
They will want more pics!
Welcome! It sounds like you’re new to old car tinkering, which is great. Forgive me if anything I say is obvious but I don’t know what you know, you know? So I’m gonna make some assumptions and try to help.
A decent floor jack and jack stands are gonna come in handy as you work on the car. I got a Duralast set from Autozone for working in the driveway. Certainly not the highest quality in the world, but good enough on a budget. Make sure you’re on level ground if possible, and block the wheels that are staying on the ground as a contingency to keep the car from rolling forward or back.
Make sure to only use a jack /stands on strong structural parts of the undercarriage. Different cars are, well different. On these, the best place in the front to jack up is the underside of the torque box on either side, and/or the frame rails. For the rear, the differential is a good strong place to jack up, and you can put your stands under the axle tubes.
Assuming you’re using hand tools, it helps to get the lug nuts started before you jack up the car. When they’re tight, the wheel will just turn when you try to loosen them by hand. When putting wheels back on, you should ideally have a torque wrench to make sure they’re evenly torqued to about 80 ft-lb. But you can get by doing it by feel, nice and tight. Again, final tightening will have to happen with the car on the ground again so the wheel won’t turn.
No need to buy extra wheels IMO. If you have a second vehicle with some space, you can jack up the Cougar, support it with jack stands, and remove the front flat tires, and either take them to a gas station to fill them up with air, or to a tire shop to get them replaced if they’re too bad to drive on. (I’m guessing you don’t have an air compressor or know anybody with one). Assuming you’re replacing all 4, you could then drive the Cougar to get the rears done. Or of course if you have 4 jack stands you could take them all off at once, if you don’t want to drive the Cougar.
Anyway those are some initial thoughts, I’m sure others will chime in too. Good luck!
Thank you! Yes, I think that I’ll get the jack, jack stands, and tires and go that route. I’m not sure the current tires or the car itself are viable for a drive to the tire store 
@Sir Ed - Thank you!
What does BL mean?
1967 Mercury Cougar 4.7L 2BL OHV 8cyl
Thanks!
2 BL or more typically 2V for 2 barrel / venturi carburetor and intake manifold on the engine versus the 4V (barrel) higher performance engine
Is this jack and stands set ok?
Duralast 2.5 Ton Jack and Stands Kit
https://www.autozone.com/engine-and-vehicle-lift/jack/duralast-2-5-ton-jack-and-stands-kit/562996_0_0
Thanks 70XR7Tom!
So BL just stands for barrel. Why was that so hard for google? 
I think that’s the same set I have at home, it works fine. The jack is a little on the wimpy side, but it’s been reliable so far and I like that it packs up fairly small in the case so I can take it with me on a trip if needed. Others will probably chime in with suggestions. If I was to do it over again and didn’t care about being able to take it with me, I’d probably still get the Duralast jack stands but maybe get a better jack somewhere else. The “Daytona” jacks at Harbor Freight look pretty good for the $. People also seem to like the “big red” jack stands. 3 ton capacity would be more ideal for peace of mind, but you’re still okay with 2-2.5. The 1967 Cougar supposedly weighs about 3000 lb, or about 1.5 tons.