Pixie,
Here's the way it will work. You're going to get a few responses and most of them will be for you to get the board the poster is riding.
My advice is this.
First of all, where do you live? What is really best is to find some people already slaloming and try their stuff. There are so many variables involved that recommending a good all-around starter slalom board is an exercise in futility. So, find some slalomers (at a race, at a session or whatever) and try their stuff.
Secondly, there's the issue of different kinds of slalom. There's wide open Giant Slalom, in between hybrid slalom and zig-zagging teeth chattering tight slalom. All boards are not good for all types of slalom.
Finally, there's PRICE. What someone could recommend as a "starter" board could end up costing over $200. Do you want new or used? Do you want a stiff or flexible board?
See what happens? The options even for a beginner board get overwhelming.
IF, though, you live somewhere out in the country or deep in the city and you're just 1000 miles from any slalomer you might not get a chance to try a board. So, READ this website. There's all kinds of stuff about decks, trucks, wheels, bearings, bushings, risers, toe stops, wedging, concave, flex, durometers, nuts, bolts and where to find the best BBQ.
I'm not going to dis' anybody but always remember to take someone's direction on buying ANYTHING with a grain of salt. Sure, Biff Strongarm who rides for Builtright Skateboards will say Builtright's full range of boards has one that's perfect for you. But until you actually stand on it and go down a hill you'll never know.
So, that's my portion of "any advice."
And don't forget: you asked for it
