Use your existing old 7 speed crankset. Get new chainrings. TA and Stronglight sells very nice ones. Expensive though. Salsa and a few others sell lower cost ones. It does not matter what gear number the rings are for, they will fit your crank and shift your 7 speed just fine. 7, 8, 9, 10, they all will work fine. Have no idea why you say rings are hard to find. 110mm and 74mm bcd 5 bolt chainrings are very common. Many companies make them. Every bike shop in the world can get them. The 110mm bcd allows rings from 33 to the 50s teeth. The 74mm bcd allows down to 24 teeth.
I have a 1991 Shimano Deore DX 7 speed crankset. I changed the touring bike from 7 speed cassette to 10 speed cassette. I replaced the rings with TA Zephyr 44 outer, Stronglight CT2 33 middle, and I have a 20 tooth inner ring. Uses an Avid adapter thing. 10 speed Shimano chain. 10 speed SRAM 11-32 cassette. Shimano 5700 STI shift levers. Shifts perfectly fine.
For you I would suggest a 48 or 46 or 44 outer ring. A 33 or 34 middle ring. And a 24 tooth inner ring. With the 12-32 cassette (12-14-17-20-24-28-32) you will have a low of 24x32. Low enough. The high will be plenty high no matter what outer ring you get. Any chainrings marked for 7-8-9-10 will work fine with your 7 speed chain and cassette and crankarms. Since your crank is 74mm bcd for the inner ring, 24 tooth is the lowest inner ring you can go.
I like chainrings spaced 10 or 12 teeth different. 14 teeth difference will also work. But 10 or 12 different makes a good difference between rings. So 44-34-24 rings is very good. With a 7 speed 12-14-17-20-24-28-32 cassette, you will use the 44 and 34 rings for 99+% of your riding. The 44x12 gear is high enough. If you need to go faster, coast. Rings of 46-34-24 will give you a little higher high, 46x12. Some might be happier with a higher high gear. If so, fine. The 24x32 low gear is about 20 gear inches. Low enough. Not super duper low, but its low enough to get a loaded bike up just about any hill or mountain. Might have to stand up and work hard for a short distance. 20 years ago I toured Europe with a low gear of 24x32 and made it up the Dolomites and Pyrennes and Alps.