In the pattern
What I need is... + {some needed action} [rather than some needed thing]
the complement will be an infinitive clause necessarily headed by "to", and the verb will express the idea of "acquire".
... to get some sleep.
If the action needed is some action you yourself must perform, then it goes like this:
What I need to do is ...
and the complement remains an infinitive clause but now optionally headed by "to", and the verb will express the idea of "perform":
... (to) tell them we cannot be there on Thursday.
P.S. You can also complement needs with an -ing form of the verb:
What she needs is coaching.
What the barn needs is painting.
She needs to be coached. The barn needs to be painted. The underlying verb must be transitive when the intended meaning is what must be done to the subject of the verb NEED. This would be ungrammatical:
What she needs is trying harder. ungrammatical
P.P.S. There are some verbs which occupy a gray middle area between transitive and intransitive:
What a good stew needs is simmering.
For this icing the chocolate needs melting.
The stew needs to simmer. The stew needs to be simmered.
The chocolate needs to melt. The chocolate needs to be melted.
Some of those verbs no longer have an intransitive infinitive when an inanimate object is the subject of NEED:
The fence needs repairing.
The fence needs to repair.archaic The fence needs to be repaired.
But we can say:
The body needs to repair and rebuild.
If you want to request [something], you would probably not use "Thank you" at the start of the sentence. It is possible to make a request and start a sentence in this way, but it might be construed as a little rude because you are essentially giving a command but hiding it in the form of gratitude.
The other option that Ronald Sole proposes in his comment is valid, but I think it is a little formal (even haughty), especially for a letter between friends.
You'd be better off saying something like:
... and if you would send me the tracking info when you get the chance, I would appreciate it.
Best Answer
As the link you quoted says, it is a very small difference. It's not really a difference in meaning, but in implication. Try this example:
This implies that the act of eating is most enjoyable. The action of eating it is the best part of the experience.
This indicates that the ice cream itself is the best part. As in, the result of having ice cream in you is what you enjoy!
Don't worry about the difference too much when you are speaking. In casual conversation, they are pretty much interchangeable.