I am familiar with the "oldies" progression I iv IV V, and the blues progression I IV V.
Apart from these, are there standard chord progressions in rock or country music? I'm looking for a way to more easily play songs I don't know.
Understand what you want, sorry, there is no one set way of doing this. But, you are correct each style of music does pretty well have a favorite chord progression. Little theory... Hang on.
The chords are put in specific spots to harmonize the melody. If the active melody line has a chord under it that has some of the melody notes in it's make up you will get harmonization. The sharing of notes between the melody line and the chord line is why the chord was put there by the songwriter. So, it kinda depends on what melody is being played as to what chord fits here at this specific spot in the song.
Take heart we can get close. If the song is called to be in the key of C. The key of C is a major key and the major chords in the key of C are the C, F and G chords. They will be your structure chords, the Dm, Em and Am are your minor chords and they are your flavor or color chords. The Bm7b5 chord is the diminished and let's not go there right now.
Most simple songs will utilize the three structure chords, in our case this will be the C, F & G. You can assume that the C will be used the most, the next most used chord will be the F and the G chord being the dominant chord in the key will probably happen one or two times per verse, normally at a lyric climax word -- so you miss it in the first verse try and get it in the second verse.
If the song starts with the C when the tune goes up scale you can assume that the F chord will catch the upper melody notes. For example:
C Scale = C, D, E, F, G, A, B, C.
The C chord is made of the C, E & G notes so it kinda takes care of the first of the scale.
And the F chord is made of the F, A & C notes so it pretty well takes care of the rest of the scale. Your three structure chords will have every note in the scale in their makeup; thus you can harmonize any song that stays in key with just those three chords. I-IV-V-I has been use in a zillion songs.
After the F chord if the tune goes back down scale the ole C is probably going to work again.
To answer your question, here are some likely chord progressions.
I-IV-V7-I
I-IV-vi-ii-V7-I
ii-V7-I
A lot of simple songs will use the same chord progression for every verse. If you know the progression for a verse you probably can use that same progression in the other verses. Probably....
Chords do two things; 1) harmonize the melody and 2) move the song along in the verse. The following will talk about chord movement.
The I chord can go anywhere anytime it wants to. However, when you go to the tonic I chord you lose any built up tension and resolve to rest. Are you ready to resolve to rest?
The ii chord is a sub-dominant chord and wants to move to a dominant chord.
The iii chord is the median chord and it normally starts a move somewhere.
The IV chord is a sub-dominant chord like the ii and it too wants to move to a dominant chord. As the ii and the IV want the same thing they can and do sub for each other.
The V chord is the dominant chord and it wants to move to the tonic I chord. Add the b7 note and make it a V7 chord and it wants to resolve to the tonic I chord RIGHT NOW.
The vi chord wants to move to a sub-dominant chord. The iii chord normally drags the vi chord with it and these two chords make a good turn-a-round progression, i.e. iii-vi-ii-V7-I.
The vii chord is the diminished chord and it is also a dominant chord and wants to move to the I tonic chord, however, is in no hurry to do so -- so it also can start a movement, i.e. vii-iii-vi-ii-V7-I. Want to resolve quickly use the V7, want to resolve, but, are not in a hurry use the vii. The iii or the vii can be used as move somewhere chords.
In a major key the major chords are your structure chords and the minor chords add flavor and or color. You are on the right track, most types of songs will have their tried and true chord progressions. Blues is I7-IV7-V7, Country is I-IV-V7-I, Jazz is ii-V7-I. Let the Internet pull up some chord charts on your type of music and see for yourself what are the most likely progressions used.
Work from chord charts right at first, and if you find yourself jamming with no sheet music, assume some stuff. If you start getting fish eyes from the guys, back to your chord charts.
Have fun.