Are there any safety data on the aircraft used for skydiving?
You didn't mention any particular country, but for the US I found an NTSB report called On the Safety of Parachute Jump Operations. It's from 2008 so some of it may be dated, but it says that no reliable data exist (emphasis mine):


  According to USPA safety records, from 1992 through 2007, about 30
  parachutists per year were killed in jumping mishaps. Safety Board
  accident data show that, for the same time frame, about five
  parachutist fatalities per year resulted from accidents involving
  parachute operations aircraft. Direct comparisons of associated risk
  are difficult to calculate due to the likelihood of multiple
  parachutists being carried on each flight and a lack of departure data
  for parachute jump operations. The Safety Board notes that the FAA
  does not have data on the number of parachute jump operators or the
  number and type of aircraft used in parachute jump operations in the
  U.S. The absence of these data precludes any calculations of safety
  statistics for parachute jump operations, including accidents rates.


Based on that information, you have 5 fatalities per year related to aircraft, and 25 that are not. So the aircraft should be the least of your worries.

Here are some key points from the rest of the report:


  a segment of U.S. general aviation operations, which, according to
  data compiled by the United States Parachute Association
  (USPA),[1]transports parachutists on 2.16 to 3 million jumps
  annually.[2]
  
  [...]
  
  Since 1980, 32 accidents involving parachute operations aircraft have
  killed 172 people; [6]most of whom were parachutists.
  
  [...]
  
  The investigation identified maintenance discrepancies on the airplane
  and deficiencies with the pilot's performance of emergency procedures;
  these issues prompted the Safety Board to examine accident reports for
  parachute operations to determine if such safety issues may be
  widespread. The results, discussed in this investigation report, show
  that these issues were present in many accidents
  
  [...]
  
  The Safety Board's review of parachute operations accidents since 1980
  identified the following recurring safety issues:
  
  
  Inadequate aircraft inspection and maintenance;
  Pilot performance deficiencies in basic airmanship tasks, such as preflight inspections, weight and balance calculations, and emergency
  and recovery procedures; and
  Inadequate FAA oversight and direct surveillance of parachute operations.
  


Anecdotally, skydiving is indeed associated with poor maintenance and hiring low-time commercial pilots. It's one of the few commercial activities that doesn't require an air operator certificate (see 14 CFR 119.1(e)(6)) so it can operate under part 91, without the more stringent rules and requirements of part 135. That also means there are no minimum hours required for the pilot as long as he holds a commercial certificate, and it's a very sought-after job for commercial pilots who want to build hours without instructing.

However, anecdotes tell you nothing useful at all about the overall safety of the industry, or about the safety of an individual skydiving operation. Some research is good and I think you can look for some common sense things that you might look for in any business: professional location, good customer service, good online presence, good reviews etc. But trying to quantify the risk in a meaningful way is extremely difficult, and you still have to balance it against the reward and against the risks of whatever else you would do that day instead of skydiving.