Personally, I would export as a high-resolution PDF and then open and convert that to jpeg in Photoshop where youhave more control than in ID's jpeg export.
If the signature is a mix of text and a logo, then it's probably better done as HTML with the logo in GIF format, preferably hosted and linked to in the HTML. This will prevent it being received as an attachment, which can be quite annoying for the recipient, especially after a few forwards when they only want a specific attachment. There's a trick to force Outlook into using the hosted image rather than producing an attachment, using the nosend="1" tag.
Except for maybe producing an initial visual, I wouldn't even involve InDesign.
Here's a guide to getting your HTML into Outlook:
Different mail clients' rendering of HTML can be pretty hit and miss, but as complete HTML novice, I found the sample HTML here to be a great basis that works well on all the clients I tried: