McKenzie gives a lecture that I really love called "Every convention you need to know to win at bridge." The lecture is all about Stayman.
I've long believed that players, especially beginning players, get too wrapped up in conventions. It becomes an ego thing just to know them, and many wrongly assume that the more conventions you know, the stronger your game is. But do you even know why you are playing those conventions? What makes them better than standard? How are they useful to you? More useful than something else? Are they super-specific and perfect for finding exactly the right contract that 0.00001% of the time you have the hand, and the 0.0005% of the time you and your partner both remember the convention when it comes up? How much are you giving up to have these things on your card?
The truth is, a lot of the most popular conventions out there are pretty worthless. They might be good when they come up, but you're often giving up a useful bid in favor of something that you might see once or twice a year. Are you really gaining anything?
Now this might seem hypocritical of me, since McKenzie and I play some pretty complicated stuff with lots of alerts, and I do love our system -- but the reason it works for us is because we have spent hours going over system notes, and hundreds of sessions honing our game. And we only add new things when we both decide we need a certain type of bid for a certain situation. I don't believe a system like ours is the way to go for casual partnerships.
For partnership desk matchups or beginning players, McKenzie and I both really advocate the KISS method. Only play things you are both comfortable with, and don't try to teach a new partner anything fancy ten minutes before your first session together. Just play the game you know, and you'll do fine. Really.
That said, I've been playing a lot lately with players who really do keep it simple, and I've found myself wishing they just played a few more things. If you're a new player looking to add a few gadgets to your card, the ones I'd want to see if you were my partner are:
1. Support doubles and redoubles. These are SO useful, and I don't really know that any other use of a double here would be worthwhile. In a situation where you have opened the bidding, your partner has bid a major suit (promising four pieces), and your right hand opponent takes a call, double or redouble by you promises exactly three card support for your partner's suit. It allows you to find a fit when your partner has an undisclosed extra piece in his suit, without getting too high in the auction before you can agree on a suit. In competitive auctions, finding a fit early is a huge advantage.
2. New Minor Forcing & 4th Suit Forcing. Like support doubles, these bids are useful for finding 5-3 fits when responder has only promised 4 of a major. I find that when I don't play these conventions, I'm constantly having to guess about partner's hand. Bids like these allow you to find your fits (or discover you don't have one) before the auction gets too high. Finding fits at low levels is also great for slam auctions, because you can now start showing controls below game. I use Blackwood about a quarter as much as I used to, and my slam bidding is at least five times more accurate now.
3. Upside-Down Count & Attitude carding (or at the very least, upside-down attitude). It's a mouthful, but don't let that intimidate you. UDCA is very simple, and incredibly useful. Think of standard carding. Now think of the exact opposite. That's UDCA. I never liked pitching a high card to show positive attitude about a suit -- you might be pitching a winner! I also prefer UDCA discards to Lavinthal and Odd/Even because with the other two, you're always showing preference for something. Sometimes, you really don't have preference for anything and you just want partner to lead the best thing he can for his hand. With UDCA, I can just pitch a discouraging high card which tells partner, "I'm not interested in this suit, and I don't have anything to encourage you about, either." With other carding, though, pard will think I'm signaling for *something* no matter what I pitch, and if he leads it, that may give up a trick when I really don't have anything anywhere. And there's something about playing upside-down count that just makes it easier for me to read a hand, but that's probably just because it's what I'm used to. I don't suspect that how you show count matters terribly, as long as you are consistent.
So beyond a KISS card, those are three things I really would insist on, as long as partner is comfortable with them. If you're not comfortable with these conventions and UDCA carding, I would recommend acquainting yourself. Support doubles and NMF/4SF hands come up all the time, and I just think UDCA is the most accurate and useful carding system out there.
Do you have conventions you can't live without? Why are they your favorites?