You're asking specifically of the (1) feasiblity of a Bavaria 50 as (2) a first boat (3) for 2 persons whom are (both?) novices to sailing.
Let me try to address your questions systematically (this is a long reply, sorry, but now you are all warned!).
My reply is based on my own ownership experiences of a Bavaria 50 (model 2008/2009) and a Bavaria 55 (model 2010) and quite a long sailing history. Still have both yachts :-)
(1a) Size: Since you plan to live for extended periods onboard, make sure to get a boat big enough that you feel comfortable inside it, in the cockpit and with a layout that suits your needs best. For example, my 50' has three bathrooms, which I find to be one too many for just two persons. Your cats might like to have their own, though :-)
Do make sure to get the boat properly equipped to help you manage it with ease, e.g. with an adequately sized bowthruster, furling sails, electrical winches and so on - this added about 1/3 (!) to the costs of each of my boats; truth to be said: they are very, very well equipped.
(1b) Make: Bavarias are at the cheaper end of the scale and as always, there is some kind of correlation between price and quality. This should be a serious consideration if you were to do Blue Water cruising in adverse weather conditions. I have been lucky to escape with only a small amount of build-problems and bear in mind that even owners of very expensive makes experience build-problems. Some Bavaria owners have been far less lucky, which brings me to the consideration of After Sales Service and warranty.
What you will experience to this end is highly dependent on the actual dealer you buy from, as it is the dealership which will have to deal with any warranty issues you might have. My study of endless amounts of blogs etc. concerning other peoples experiences plus my own practical experiences can be summarized to just four words: prepare for a marathon.
(2) A 50' as a first boat: In my opinion, a big boat is like a big car: the first few times you drive it and park it, it is a bit hard to do it precisely and with ease. Then you get used to it and you no longer even think about it as being a big car ...
But, as others have written: Big boat - Big costs - Big trouble.
Everything on a larger yacht becomes exponentially more expensive and this goes for marina costs as well. In the Med, berths are available, but the bigger the boat, the fewer the available spots.
I noted your (economical) rationale for getting a big enough yacht as the first one and someone wisely commented that "you don't know what you don't know". Even with years of practical sailing experience and meticulous studying and planning before buying the 50', I think I would have chosen differently today, just 4 years later. So do not bet all that you will just buy "the one" boat and then that's it ...
(3) Novices to sailing: As long as everything goes well and the weather behaves, no size is too big. But when the weather turns sour or something breaks, then everything is much harder to man-handle on a big boat. This is where experience comes in handy and may save or compensate the situation. From personal experience, I can recommend hiring a professional skipper and spend some time sailing with him/her to learn first hand from their hard earned lessons on the big oceans.
Am I happy with my 50' and my 55'?
Considering that I knew quite well the trade-offs of getting a relatively cheaper make of yachts, and that I would want to and need to make a lot of upgrades, then yes. What surprised me the most is the (lack of) after sales service and the builder's (lack of) concern for its customers.
Congratulations: you made it to the end!
Feel free to contact me for other aspects of optimising your first buy of a yacht.