As far as rebuilding, the most critical components on the carbs are the throttle shafts which wear and leak air. There is an e-bay vendor in Italy who sells just about all the parts for these carbs, including new oversize throttle shafts. It's a lot easier for the rebuilder to install these vs. installing bushings. All the gaskets etc are available.
The Solex PHH carbs all differ between the various BMW models, 1800ti, 1600ti and 2002 ti. The 1800ti versions are older and have very short emulsion tubes, if you can even call them that. If you have a 1600ti, I would advise you to start with 1600ti specific PHH 40s and get them rebuilt. If you had them rebuilt and they were just sitting, all they need is a good cleaning and maybe some new gaskets. And, if this is the case, this shouldn't cost much.
Back in 1983 I got my set of 1800ti carbs hot tanked. The bodies of the carbs came out with a hint of green tint. The air horns or trumpets polish well, but the 02 specific trumpets are angled. And, some appear to have a rougher finish.
On several occasions I've recounted how I obtained those carbs in Hollywood from a guy who had three 1800tis sitting in his driveway. You entered his bungalow by using one of the cars as a step. He sold me the carbs for $100 or so, air canister included along with linkage and manifolds. And, he threw in one of the 1800ti's for FREE. He had cannibalized the head from it, otherwise it was complete with an excellent interior in Red & Black. I just grabbed those front seats and left the car on the street as I didn't have the resources to get it towed back to Burbank. I was just 17 years old. When I got home I realized the NK seats were too wide for my 1600. So, I gave them away to my friend who was getting his Olds Cutlass back on the road. He installed them in that red Olds Cutlass and eventually destroyed them. In short time he parked that Cutlass, as it drank a lot of fuel, and purchased a solid 1963 Porsche 356 B model for $2,500, which he used as daily transportation to college. After taking turns commuting my friend realized my 1600 was much more practical than his 356. By 1986 he found a solid 1971 2002 for $1,400 and used that car as his daily driver for the next 10 years.
1800tis were dirt cheap and sometimes FREE. I also came across a few 1600tis. One was being sold, minus the motor, for $300. And, the body was solid. There was one up for sale in Glendale, CA about 15 years ago. The guy was asking $8K for it, but he had cannibalized the door cards and replaced them with ones from a later square model car. He had also taken off the rear bumper and replaced it with a US federalized style from 68. He was cannibalizing parts from the 1600ti for his Cabriolet restoration. The car drove well, though. I test drove it. It still had the original motor and carbs.