There are a few criterion to consider when choosing the Keyblade that you want to spend your limited resources strengthening. These considerations are as follows and will be addressed in the order listed:
-Maximum Potential: Based on buffs and debuffs what is the Keyblade's maximum potential?
-Medal Affinity: What medals do I have so that I can choose a Keyblade that will provide the best multipliers for it?
-Enemy Affinity: How effective can I expect it to be against different types of enemy?
-Availability: Do I have the Keyblade already, or will I need a strengthened Keyblade to even obtain the one I want?
-Layout: What strengths are gained from the medal type layout?
Form these criterion there are, in truth, only a few keyblades worth strengthening because of how the current meta works. These Keyblades are:
For reference: U=Upright, R=Reversed, P=Power, M=Magic, and S=Speed
-Starlight (UM,US,RP,US,UM)
-Sleeping Lion (US,US,RS,US,US)
-Counterpoint (UM,RM,UM,UM,UM)
-Fenrir (UP,UP,UP,RP,UP)
-Darkgnaw (RP,UP,RP,RP,RP)
-Missing Ache (RS,US,RS,RS,RS)
-Diamond Dust (RM,UM,RM,RM,RM)
Maximum Potential:
If you look at the keyblades I have selected you will notice one very important thing: each one is set up such that there are either 4 Upright slots and 1 Reversed slot or 4 Reversed slots and 1 Upright slot. This is VERY important because the major strengthening medals (Illustrated Kairi [EX], Illustrated Xion [EX], Scrooge McDuck, etc) all give buffs for either Upright Strength/Defense or Reversed Strength/Defense in addition to normal Strength, Defense, etc.
Therefore, in order to make the most of your Keyblade you will want to choose one that allows you to apply an Upright or Reverse buff to as many medals as possible. All the Keyblades not listed above have either a 3 Upright and 2 Reversed setup or a 3 Reversed and 2 Upright setup. This means that you end up losing damage multipliers on either 2 or 3 of your medals as opposed to only 1 of your medals as in the case of the recommendations above.
Medal Affinity:
One keyblade listed above is easily more capable of fitting with the medals you draw than the others. That is of course Starlight. Starlight can use Magic, Speed, and Power medals which increases your chances of drawing a medal that you can use in your strengthened keyblade as opposed to the other type homogeneous keyblades.
Enemy Affinity:
Enemy affinity for the keyblades listed above is split drastically. Starlight is capable of fighting against any enemy but isn't particularly strong, or weak, against any particular type. All of the others listed are tailored to fight one type of enemy with a massive advantage while being acceptable for a second type and significantly weakened against a third.
Availability:
Starlight is your starting Keyblade and therefore is by far the most easily available. All the others listed require you to complete hard mode quests which will require multiple strengthened Keyblades.
Layout:
Of the Keyblades above Starlight, Counterpoint, and Diamond Dust benefit the most from their medal type layout. This is because traditionally the strongest buff and debuff medals have been upright or reversed magic medals and the sooner you are able to use those medals during your turn the better. These three keyblades allow you to use those medals in the first slot or second slot while providing a strength boost to the medal.
Conclusion:
You will notice that in every section Starlight was mentioned... this is because Starlight is in fact among the most useful and most powerful keyblades that you will obtain. It is well worth your while to strengthen this keyblade to level +35 first, and then use it to gather the resources needed to strengthen other keyblades. Any of the keyblades listed above are worth strengthening to level +35, and any keyblade not listed is worth strengthening to at least +25 (as the materials needed to get to level +25 are not hard to obtain).