Align selected objects to a guide

Aligning point text is easiest to do using the starting anchor point, which is at the left, right or center of the text depending on the text alignment. Since your text is visually centered and you want to center them with other objects you should set the text alignment to center.

You can then turn Smart Guides on (View → Smart Guides or cmd+U) and snap the text objects to your guides. Notice it’s the beginning anchor that snaps to the guide:

As for aligning arbitrary objects, the easiest way is to select everything you want to align (including the object you want to align to) and change the “Align to:” in the Align panel to “Key object”; you can then click the object you want to align to (which will give it an additional highlight) and use the regular align options.

For example:

Another thing that may or may not help you when aligning text is the “Use Preview Bounds” option found in your preferences.

Normally text is aligned using the bounding box of the type which is controlled by the font itself, if that is giving you undesirable results you can enable the preview bounds option which will instead align based on the visual paths of the type (as if you had outlined the type).