What kind of love is Touchstone most interested in?

The short answer is the physical kind. Touchstone, the court jester, is a cynical old so-and-so who does not have much time for the courtly, romantic variety of love displayed so fervently by Rosalind and Orlando. Indeed, the much earthier, lust-driven attraction Touchstone feels for his dim country girl Audrey acts as a foil to the passionate love of the two leads.
Touchstone and Audrey are in so much of a hurry to get married that they perform an impromptu wedding ceremony under a tree. Ever the cynic, Touchstone instantly recognizes that since the "wedding" is informal, he may continue to engage in multiple affairs with impunity and one day leave his "wife." Cynicism aside, Touchstone is wise enough of a fool to understand that a relationship based purely on sexual lust cannot last for very long. A similar degree of insight is sadly unavailable to the hapless Audrey.
Contrast this with the long, drawn-out courtship of Rosalind and Orlando, which has all the hallmarks of a traditional romance. And yet even Rosalind eventually comes to tire of Orlando's devoted wooing, wanting something much deeper from their relationship. Touchstone, as we have come to expect, has a cynical contempt for the convoluted game being played out between the two young lovers:

The truest poetry is the most feigning.

To Touchstone, it all seems so terribly dishonest, this love business. Rosalind agrees to a certain extent, which is why she sets out to test Orlando's love. But unlike Touchstone she is not a full-blown cynic when it comes to romantic love; she still believes in its magical properties.
The contrast between the two kinds of love sets up a choice as to which is the more honest. On the one hand, we have the bawdy, unrestrained lust of Touchstone and Audrey. Yes, it is pretty tawdry and more than just a tad indecent, but at least there is a simplistic honesty and openness about it. Say what you like about Touchstone and Audrey but there is nothing remotely artificial about their particular brand of love.
Then there is Rosalind and Orlando. They woo each other so beautifully, reciting love poetry and carving their names on trees. It is all so decorous, so wonderfully romantic. But isn't there just something rather fake and old-fashioned about it? They may well be acting out a long-standing tradition, but since when has tradition had anything to do with the beauties of love, in all their majestic wonder? And where is the honesty when both lovers constantly need to put on emotional masks as part of their tiresome, drawn-out courtship ritual?
Touchstone's idea of love may not be to everyone's taste. But, all things considered, we can still at least appreciate that it has a certain rough-and-ready appeal.