Is a Mooney M20 a difficult plane to fly as a beginner?
You need to be a bit more specific as "M20" refers to a lot of aircraft. An older M20C or M20D (with the fixed gear) should be quite manageable. An M20TN Acclaim is out of the question. Since you mention 60K I assume you are talking C/E variant but clocked out J's can be had for that. You can likely find an A/B but wooden wings are not for new owners or the faint of heart. 

I have a Private Pilots License, an Instrument Rating, and a Complex Endorsement (which you need to fly just about any Mooney aside from the fixed gear D model) and have been pretty seriously looking at buying a Mooney as well as flying a few. Here are some thoughts:

The older Mooney's are on par with the other various trainers (PA-28/C172) size and load wise but tend to be about 10-15% faster on 10% less fuel. When it comes to flying, speed is generally what makes an aircraft "harder" to fly. The faster you go the faster things happen and the more likely you are to make a mistake or enter some airspace you shouldn't. In a Mooney, which is generally a faster plane you are of course more likely to have these issues. 


You need to consider when training in a complex aircraft you are adding two additional things (gear and prop control) to an already confusing environment which can add to training time and increase your chances of messing something up. 
Buying an aircraft for training can save a lot of money in the long run but what if you end up not liking it? 
Although rentals are not always super well equipped in my experience they tend to be pretty well maintained as the flight schools are in the business of making money, so you dont lose training to the fact that you cant afford some AD or other maintenance issue.  
Insurance premiums on a complex aircraft may be high for a new pilot. I can tell you that premiums for an M20C/E once you have your license are reasonable. 
Mooney's have their own maintenance quirks but with the recent PA-28 spar issues that pretty much every GA plane has some kind of pricy issue.  
You may want to define 2-3 passengers a bit better, a significant other and two kids is a lot different than 3 other "buddies". The back of most light aircraft is not exactly the most comfortable place. 


I would take a serious look at this guy's thread he has a D model he has been working on for some time. The tale is a good example of what you are in for.