This is a most interesting posting! Just let me say 5 things.
- The Arduino is not really a construction set with easy building blocks. There are many breakout boards available (best look at sparkfun.com!), but not for everything. Especially the TCs will need special amplifiers and extent software...
- "How many" it not the best question. The correct question is "how many AND how fast". With little and cheap external hardware hundreds of transistors or SSR can be handled, but not on a 100 microsecond basis. This in fact will make the ballance: Use a Mega-Arduino (really enough lines?) ? Use the much better supported standard Arduino (+ hardware extensions)?
- Though the first steps are simple it will need more and more expertise when you drive the Arduino to its limits. I am sure you know more than you have admitted, but I doubt that you can cope with the involved software issues. This is not so much a matter of knowing or learning, but of practical experience...
- You might need a robust and hardened board; luckily one of our forum members here has such a thing..
- The Arduino concept, when applied with discretion, will be the best price-performance relation I can think of; where I do not only consider the hardware but also the programming efforts and community support...
Obviously this is just my personal opinion....
Much luck!