Yippee! A rhythm question!
For practical purposes (at least to begin with, until the rhythm sinks in properly) you should count 6 quarter-notes to the bar as both Chris and Andrew suggest, but of course not as two groups of three (ONE two three FOUR five six) but as three groups of two (ONE two THREE four FIVE six), because eventually you want to try to feel 3 very slow pulses (half notes) to the bar without too consciously subdividing them.
The difficulty is that you can't really do this until you get to bar 3, because in the first two bars the situation is complicated by those troublesome triplets.
All you need to know is that the three triplet "quarter notes" add up to the value of a half note, and therefore the whole note should last exactly twice as long as the triplet group, that is to say six times as long as each triplet note. Unless I'm misinterpreting Andrew's notation, what he says
[(whole note)=12] [(lh triplets)=3]
is wrong, his 3 should be a 2.
Before you begin, decide how fast your main quarter notes are going to be from bar 3 onwards.
Subdivide each of them into 3 pips. Then two of those pips is how long each of the triplet notes in bar 1 should last. But you may be better just feeling the 3 triplets instead of counting two pips for each.
When you get to bar 2, just hold the whole-note for six of those triplet pulses (or 12 pips if you prefer).
As you approach the end of bar 2, reinstate the pips (unless you've retained them) on the last of triplet notes so that you can get the relationship right as you switch to the "proper" quarter notes in bar 3. Each real quarter-note then gets three of these pips, and you should then be at the tempo you decided before you began.
As soon as you've played the first few notes of bar 3, forget the pips and just use those quarter notes as your basic pulse from then on, so that in bar 7 the dotted whole note gets 6 of these pulses, and then in the 5/4 you continue with the same pulse, except that each bar gets five of them.