Is there a technique that's kind of standard or should I just play around and do it according to my own taste?
The answers here are yes and yes.
Typically (though not exclusively), bass, drums and vocals go down the middle, other instruments are panned left and right according to taste.
Ctreating a stereo image is tricky when it's just vocals and a piano (or guitar). You can increase the apparent width of the sound stage by recording the keyboard in stereo (most contemporary ones have stereo or mono outputs). This puts vocals in the centre with the keys kind of surrounding it. You can also use stereo reverbs to fill the extreme left and right of the sound stage.
You can put high and low congas slightly left and right, and similarly, you can spread the kit left and right as well.
There are, in my view, two primary rules:
1 arrange the instruments so that there is a good balance (of dynamics as well as sonically) between left and right.
2 arrange the instruments so that a listener can make reasonable sense of the performing stage*.
You will get an idea of what to do by listening closely to the instrumentation of your favourite tracks.
* I posted this, then reread it, and realised I have contradicted myself. I said "arrange the instruments so that a listener can make reasonable sense of the performing stage", but earlier, said "You can put high and low congas slightly left and right, and similarly, you can spread the kit left and right as well." When you examine this advice, you will see that this puts a drummer and a conga player both in the centre of the stage, and it might put the congas so far aprt that a conga player wouldn't be able to play it! Well, all's fair in love and music, and rule 3 could be "break rule 2 if you want to, and it still sounds good".