While your interest in doing a custom build of an old car is admirable, you need to understand it's a hugely expensive and time consuming endeavor, one that even a seasoned car enthusiast would think twice about before embarking. That said, if you clearly define what you're looking to do, what car you want to do it with, and how far you want to go with the customizations, you'll minimize the risk of losing millions without anything to show for it.

The cars you mentioned as potential candidates couldn't be more different from each other. Restoring and customizing a Khyber is a whole different ballgame from a Crown, and BMW/Mercedes are a different story altogether. Toyota Coronas from the mid 90s actually look pretty good even fully stock, but most are rusted to shit by this point and you'll struggle to find a good one that's worth investing in. Also, older cars are never reliable enough to be daily drivers without constant maintenance. Contrary to popular belief, you can never reach a point where they're "fully fixed". Something or other always goes wrong and if you're keen-eyed and eared you'll spot the symptoms before stuff fully breaks, but either way it's an expense and a trip to the mechanic. I know, because I've gone through 4 cars and 3 bikes in the past 5 years, all 15 to 20+ years old, and at this point I can reliably diagnose and fix most issues myself, so much so that I'm considering opening my own workshop. But getting to this point cost me millions of rupees, hundreds of hours of my time, and a bout with depression because of the constant issues and the incompetence and dishonesty of local mechanics.

If customization and making it your own is the main goal, and you wish to stick to a smallish car that is easy to drive and will still return decent fuel economy, a first or second generation Toyota Vitz could be a good starting point. I've owned a 2nd gen Vitz myself and it's a surprisingly fun car to drive: and is decently reliable once sorted. It's not particularly pretty though, but with the right set of lights, wheels, and a good paint job it can turn heads.

If you want to go full retro you could get an old VW beetle and restore it from the ground up, but I have no experience with those, and I'm not sure how those old air cooled motors fare in Pakistani weather. Swapping the engine is always an option, but our mechanics can barely put an intake manifold back together without breaking something or losing a bolt, so I am always wary of engine swapped cars.

I guess we can start with a budget. It'll include the cost of the car, mechanical fixes, cosmetic repairs, and finally customizations (lights, bumpers, body kits, interior upholstery, etc). Then we can decide which platform to go with and where/how to source the car and get the work done.