I know everyone plays it differently when it comes to gm but, is movement distance something I need to be critical over? If so then I would feel the need to make PC's take a standard action to put on and take of armor which seems like a waste. I am still pretty new and wanted to ask more experienced gm's or other people's play styles they have experienced and can say if they were good or bad.
Movement Speed Matters
Movement speed matters. If you're a low level caster with very limited HP and want to cast a spell, you don't want some melee guy taking attacks of opportunity when you do. If you're that melee guy, you don't want to let the spellcaster get away so he can cast freely.
The movement speeds relative to each other matter in that kind of situation. In my experience, a player who dies because we didn't worry about movement when they could have used their speed to survive is not a happy camper. I can't blame them.
This is pretty easy to track if you're using miniatures and a game board. If you're using a less formal method of tracking positions in combat, it gets trickier, but a fast character should never be penalized relative to a slow one, no matter what method you're using to run your game.
Armor actually takes multiple rounds to put on and take off. Full plate takes minutes. I've played in games that track this strictly. I don't do so in mine, as the party tends to camp in a secure location. It's assumed they put their armor on before setting out for the day, and the players are content with that.
If they got caught in an ambush while sleeping, then it would matter. Most of the time it's not something I find is worth worrying about.
A good default assumption (applies to many games): Understand and use the rules in the book, unless you have a good reason not to. If you do have a good reason, be consistent according to that reason,and spend a little time considering the consequences. It may help if you discuss changes as a group, so that players don't think you are playing favourites, or can be argued into changing rules that inconvenience them at the time.
On the specific rules for armour, this only really crops up on the battle board, or in chase scenes where speed matters. Pathfinder has rules for getting in and out of armour which are a little harsher than 1 action suggested in the question.
In my games using battleboards, chases or long-distance travel, I have found it helpful to stick to the rules as written for armour speeds and penalties. It gives another dimension to characters - they can choose to play mobile-but-less-well-defended, or heavily-defended, but slightly slower characters, and the difference plays out during the game.
Having said that, allowing Fighters and Paladins better options for getting in and out of armour generally will not hurt. Those classes are very dependent on their equipment and are considered quite weak compared to others in the game.
Note that ignoring speed differences for sake of easier play will also invalidate some magic items, class features and spells. It should be fine, the game has more depth than just speed and movement numbers, but do let players know before they create their characters, otherwise they might choose to optimise character speed or mobility to discover you have made that not relevant to your game.
Generally speaking, there are only three movement speeds that matter: “slower,” “faster,” or “dead-even.” A faster character can get away from a slower one, and catch up with a slower one even when the slower one has a head start. A slower character cannot get away, and even loses any space they had if a faster character presses. When two characters are even, you can’t get away, but an opponent cannot get closer to you if you keep mirroring his movement, either.
Since most characters have 20 ft. or 30 ft. movement speed, armor which drops you from one category to the other is kind of important – or, as important as movement speed gets, anyway. But remember that the statements I make above are only true if everyone has ample space to maneuver, and assumes that the combatants care about the spacings between them, which may not be the case.
So if you wanted to play loose with movement, I would note the effect of armor, and just mentally keep track of armored characters as being in the “slower” category.
I have never actually had call to use the rules for putting on armor. Characters in my games tend to take measures necessary to ensure that their armor will be available when they need it (wearing light armor, having Endurance or a restful crystal, some other class feature, etc.), and even in the cases that they don’t have their armor, they just do without, not attempt to put it on in the heat of battle.
If it makes GMing more difficult for you or is not important to the story, you should consider ignoring it. (Assuming you have no players rely on this mechanic).
That said, movement distances in combat is important. A lot of strategies and mechanics are based around combatants only moving a certain distance per turn.