First, make sure you read and understand the basics of doing training on your own aircraft (vastly depends on where you are planning to do it, some places won't allow that without humongous administration ... and fees, or do not allow it at all unless your aircraft is under CAMO ATO).
Second, understand that learning is easier with less complexity. A 172 fix-propped is much easier to learn on, than a 182 CS.
Also keep in mind you are stressing the aircraft during training sessions, as you may never do so later on. I prefer to ride the old school whores in basic training, as it does not hurt that much, if things go wrong. In the end these air-hookers are fine for learning, but don't take'em home for more ;-).
One more thing. There is almost no way at all to estimate what your flight profiles will be after PPL. Whatever you dream being a pedestrian, may differ from what is wise later as an airmen. Try different aircraft in training, do hours in C150, C172, PA28, AT01 or whatever you can get your hand on. After PPL rent and learn. You may find yourselves need shifting. You may be well later with a C172 and would have regrets to spend the premium over it for a 182. Or you find out the best plane for you is a G36, what are you going to do with the premature purchased 182? Things are only little predictable.
A word to the often cited Reims Rocket/Hawk XP and C177, even worse 177RG. Once upon a time, there was a saying these birds would offer the performance and usability of almost a 182 at 172 costs. This no longer holds true. Where spare parts or replacements needed are special to these birds, prices have gone through the roof and some very special parts may even no longer be available. One of the biggest shots I heard lately was an over 3.500 USD price tag for a small and simple break fitting special for the 177RG - and with an 8 month delivery estimate - not very unusual i.e. for non-hydrolic RGs. These birds were built in small numbers and where parts are special, things will get worse and worse.
But, in the end all advice is for the wind, as it comes down to personal preference and nobody can compensate for a thing almost forgotten in the rest of society - individual freedom of choice.