I think I will try to for once in my life finally play all through this game and beat it but I want to know one thing before I start... does it matter when I upgrade my classes? Do I get more stats by upgrading as soon as possible?
As to say... and I have no idea of the right numbers but say I get to Lv.30 and then class change and my HP is 300? Again keep in mind I don't know what HP will be at a certain level. But anyway say I class change at Lv.20 and when I become Lv.30 then my HP is 400. Is that how it works?
So yeah I know I didn't have to explain that but well... yeah does it matter if I upgrade early? If so... what is the lowest possible level on normal mode to try this?
Stats like HP, MP, Strength, Vitality, Intelligence, Agility, and Luck are not affected by class change. At least, not that I'm aware (can't be 100% sure of the internal workings of Origins, though). However, Magic Defense - a hidden stat - is, for at least one character. Probably.
This is likely only relevant if you have a Monk. On the NES version, Monks had +4 Magic Defense growth per level, but Masters had +1. Yes, you read that right; the advanced class is worse than the basic class! Magic Defense growth rates were generally pretty screwy on the NES, and the Monk/Master dynamic was the most clearly bizarre. So, for that purpose, it's actually better to put off class change for awhile. There is a slight tension if you have a Warrior or Thief, who gain spell charges upon class change, but have to class change early enough if they want to get all four possible charges. Mind you, as long as you class change before L43 (which is about 15 levels higher than you need to be to beat the game), you'll be able to get all four charges.
The ambiguity here is that I don't know whether Origins may have altered any magic defense growth rates (since it is a hidden stat), and if they were going to alter them in terms of "bug fixing", the Monk's/Master's would be the most likely one they'd alter. So, you could be hesitant to class change a Monk based on the NES version, but just know that there is a chance that this was changed for this version and you might not be helping, or even doing some harm, by waiting.
But apart from Magic Defense and Spell Charges, there is no permanent difference as to when you class change. So, no hurry.
Just to add to that...
The Fighter and Thief upgrade to Knight and Ninja respectively. These are the only two classes that gain magic on Class Change that had none before. Upon Class Change, they can immediately learn all the spells available to them (you can buy them all at the magic shops), but they have no charges to cast them. They gain one spell charge whenever they gain an odd level 15 or above. For example, if you get Class Change at level 18, when you level up (to Level 19), your Knight and Ninja will have 1 spell charge for all the spell levels they are able to use (1-3 for the Knight, 1-4 for the Ninja). They max out at 4 spell charges.
That's really your only motivation for getting Class Change early, but no other stats will be affected aside from the Magic Defense on the Monk/Master that Astral mentioned.