I am the marketing coordinator there. Just go on our website and click on schedules then club events and info. It should give you all the car club related info you need including track dates and club contact info.
I am actually doing my first track day with the SCDA on June 23rd with my SVT.
There are over 200 various driving events at Lime Rock Park each year.
Also this memorial day weekend is the Rolex GT Series Challenge. Grand Am, Formula BMW, American GT, and the Mazda MX-5 Cup will all be racing this weekend. Also the Hemmings Sports and Exotic Car show on Sunday (no racing on Sundays).
Monday the 29th is the best day to come since both Grand Am GT and GS classes will be racing along with a host of support series.
Don't really know what you have done, but I would highly reccomend to get some experience at an autocross before heading out onto the big track. It'll quickly teach you about the proper lines and how your car behaves at speed and in racing-type manouvers. If you already have that covered, Lime Rock is awesome! Especially if you can get yourself in on an organized track day with experienced drivers to help you out.