Veteran gamer. New to Kingdom Hearts. What difficulty mode?

Normal. Always start with normal to gauge yourself. KH1 had a lot of thought and variables put into it so some of the difficulty will also depend on what weapon you pick at the start since each weapon sets a different ability line. You have the same abilities, or most, in all options but it does dictate which ones you get early.
Like picking the shield will get you support abilities faster.
The weapons also affect stats a bit since if you chose to discard the staff you have like one mp bar at the start or if you pick it as your main choice you'll have three.

Beginner is almost universally too easy and Proud will depend on the person so I recommend Normal and seeing what your play style is. KH gets a lot of flack for button mashing but the thing about KH1 and 2 is you have a surprising amount of options. More so in Kh1 with enemies.

Like the easy way is to just smack everything with the keyblade but if you use magic you'll learn that some enemies in KH1 are weak. Like fire heartless hate ice or heavy heartless take lots of damage form gravity and then there's stop which is just damn helpful in all areas.

Summons kinda suck save for little material gathering tricks. The only useful one is Tinker Bell which you get near the end of the game. She heals you, revives you once if you die and doesn't make your Party Members vanish.

I'm rambling haha just pick normal and learn what your style for Kh1 will be.

Any kingdom hearts game is essentially as hard as you make it for yourself. Later games even have options for zero exp. The 1.5 version of Kh1 has it in fact but dont even go near that yet. lol

 

Normal difficulty is fine for a casual playthrough. Proud Mode gets worse, especially if you don't know what you're doing.

Random Stuff to Know:
1) In the beginning you are given a choice between three weapons (Sword, Staff, and Shield). Pick one and get rid of one. Not only does each weapon influence your starting stats, but they also effect your leveling up. For example, if there's an ability you learn at level 9 if you picked the sword, you would instead learn a different ability at that level for the staff and the shield. If you decide to do a Proud Mode run, picking the shield and getting rid of the sword is generally agreed upon to be the best option (At least elsewhere on the internet that I've seen).

2) The strength of your magic spells are dependent on the amount of MP you have. More MP = Stronger magic.

3) At some point during the beginning part you will be asked three questions (I don't remember what they are). Each question has three separate answers. The answers you pick determines the rate of exp gain. If I recall correctly, one set makes it so you require less exp until you get to level 40 and then require more experience after level 40 while one other set of answers is the opposite.

4) While you get most of your spells throughout playing the game, certain spells (Curaga, Aerora, Aeroga, and maybe some others) require doing something extra. In the case of Curaga, you simply have to talk to an NPC at a certain point. The two Aero spells are found in a treasure chest and for doing some portion of the 101 Dalmatians sidequest.

5) The Aero spells are defensive. Cast them and you will take less damage and enemies will be hurt when they touch you.

6) I don't remember if they fixed it in the 1.5 remix, but there is a red trinity spot that is missable forever if you complete Halloween Town before you use the trinity spot.

 

^ That trinity spot was fixed. It appears on the ground after you beat the boss.