The link I posted in the comments gave a good explanation on how chords resolve best in a major key and I will reiterate that and explain in general what is preferred in an progression.
Let's start out with common tones as touched on by user2808054. I will be using C major as an example, but also put the Roman numerals so it may be reproduced in any major key.
The most amount of movement between notes will always be going up or down a 2nd. There are no notes in common between triads up or down a second.
C - Dm - Em - F - G - Am - Bdim - C
I - ii - iii - IV - V - vi - viio - I
When you go up or down a 4th, the triads will have one note in common.
C - F - Bdim - Em - Am - Dm - G - C
I - IV - viio - iii - vi - ii - V - I
The least amount of movement between notes will always be going up or down a 3rd. The triads will have two notes in common.
C - Em - G - Bdim - Dm - F - Am - C
I - iii - V - viio - ii - IV - vi - I
Going up and down a 3rd makes the smoothest transition, but you do want some motion in your progression and using too much of one type of movement will make the progression sound predictable and dull.
Where chords want to go
MusicTheory.net gave a wonderful, wonderful graphic and explained where certain chords want to go in a progression. In the key of C major this would be:
Em -> Am -> [F or Dm] -> [G or Bdim ( -> Em )] -> C -> ANY
iii -> vi -> [IV or ii] -> [V or viio ( -> iii)] -> I -> ANY
As you can see there is usually common tones moving from one note to another, but not always. These are just general guide lines, but they do sound good.
In any progression, you would want to start with I and end with some kind of cadence. The most typical cadences are half (ANY -> V) and an authentic cadence (V (sometimes viio) -> I).
A typical progression is usually a multiple of 4 measures long and the cadence will usually consist of the last two chords play and may be in the last two measures or last measure depending on the harmonic rhythm.
There's a lot that you can play around with and try and use all of it. In short use a mix of large, small, and no motion and always start on I and try and end with a cadence and your progression should be fine.