Executive or Short courses are usually 9 (sometimes 12) holes, many par 3's, some par 4's and 5's. It's like the last step before playing a full, 18 hole course (preceded by pitch and putt and long par3 courses) or if you don't have 4.5 hours to play a full course.
Par 3 course is just that, 18, par 3 holes. The difference between a Par 3 and pitch and putt, is that a Par 3 has longer holes, different obstacles and the grass is generally a lot nicer, with better scenery.
Meridian Golf Par 3 - South Surrey BC - Home
In terms of equipment, I think you should piece together some good quality, brand name, used/demo clubs and bag and some new shoes/glove. Since they're already used, you won't take such a huge hit if you decide the game's not for you and re-sell them. Are you a righty or lefty btw?