Another great tip I got directly from Steve Bailey (plays a lot of chords) is to almost always use your middle finger for the root note. You can easily play 7th chords this way by omitting the 5th. Unless you're going for a root/5th thing, you can pretty much always omit the 5th because it's not really adding to the tonality (major, minor, dominant) of the chord unless it's a flat 5th.
For 2 note chords (double stops):
I use this technique for root/5th, root/3rd or any other combo you may like (root/octave, root/6th, root/9th, etc). Technique wise, I just go with what's comfortable but always bear in mind where I'm headed next. I will use my index finger or middle finger for the root depending on where I need to go afterward. The goal being to have a very smooth transition from the chord to the next note (or chord).
I happen to play a lot of 3 note chords, and this is how I do it:
Again, use your middle finger for the root. It puts your hand in a much better position for the chord and also gives you the option of moving up or down the neck easily because your index finger is ready to go down and your ring and pinky fingers can move up with ease.
With the root on the E string, you play your 7th on the D string and your 3rd on the G string. This creates a very nice voicing that makes the 3rd really sing because it's on top (the highest pitch). Yes, it's an inversion, but to my ears inversions often sound better on bass. Plus, they let you imply a melody at times which can be very interesting.
With the root on the A string, you play the 3rd on the D string and the 7th on the G string. This is more standard (not an inversion), but you're limited so you kind of have to do it this way. It's very easy to go from a root on the E string chord to a root on the A string chord so moving harmonically in 4th's and 5th's is really simple, which often happens in western music.
Here is a quick example in case this^ was too difficult to follow:
Playing an A minor 7th chord with the root on the E string, you'd use your middle finger for the root (A), your ring finger on the minor 7th (G on D string) and your pinky on the minor 3rd (C on G string). Yes these are all on the same fret (5th fret), but do not bar them because it locks you up for passing notes.
Now for the A string chords, I'm going to use a E7 (dominant) because this creates a II-V progression which is very popular, so it will sound common to your ear. Use your middle finger for the root (E), your index finger for the major 3rd (G# on the D string) and your pinky on the minor 3rd (C on the G string).
In the above example you do not use your index finger at all, this is a good thing because it leaves your index finger free for quick jumps to your next note. Will make your transitions much smoother at higher tempos. Keep in mind, chords sound better the higher up the neck you go as they are less muddy. As for hand strength, that will develop as you work on this more. Also, you eventually realize that these are just hand shapes, not unlike guitar chords, and once you learn them you can use it as needed anywhere on the neck.
You can always apply these principles to any Major 7th, Minor 7th and Dominant 7th chords on either the E or A strings. As you get better at this and enhance your harmonic know-how, you'll eventually learn to apply this to other odd chords, although they may involve your index finger. For triads, you can simplify drastically and just use the Root/3rd. Or feel free to try to do a root/5th/3rd for a true triad, but it's not pretty and doesn't add much. For true triads, you may have to abandon the middle finger approach, just FYI.
Good luck! Chords can be very musical, especially in a small combo. I know it changed my playing and even helped my song writing. Also very useful for my walking basslines because I began to hear the harmony more clearly and could easily identify the important notes of a given chord.