Don't split them up into a million things as being suggested. Unless you strike the jackpot, it'll set you back considering the fees and all that. Find one or two coins that you are feeling happy about, and do indeed research them well. Look at recent chart statistics, speculations, recent behaviours, etc. When you find two coins that are doing well, go to an official exchange and fully verify yourself to allow for maximum exchange rates and the best offer from them (least fees, higher limits, etc.)
In my opinion, now is a horrible time to invest in Bitcoin. I have a feeling it's going to be crashing real soon, and if it does, that's the golden opportunity to strike.
As for the actual investing the money, any major exchange could fulfil the orders.