I want to complete Mass Effect 1 and import that save into Mass Effect 2 without having a love interest appearing in the picture frame on Shepard's desk. What must I do in Mass Effect 1 to achieve this?

In the ME wikia it states that it is possible by not talking to a potential love interest but I don't want to miss out all those experience points and other goodies. It also states that it's possible by leaving that love interest on Virmire.. but I don't think that's of any use if the love interest happens to be Liara.

I'd assume (though I don't rightly know) that avoiding extraneous conversation with any of the possible love interests in the first game will pretty much allay your concern. And you can make up the necessary experience points doing planet-scouring bullshit. Besides: 
 

I think either you're going to have Liara as your love interest or you're not. I can't think of a way to get all those "other goodies" and not end up with her in the picture frame.

First, don't romance Liara. Once she's locked in, there isn't much you can do aside from starting over. How romance transfer works is very finicky. Even if you reject them when they come to your room the game will still say you're in a relationship with them in ME2. In order to not have a romance transfer, there are two ways. One is to never talk to them. Ever. Even talking to them once and saying the paragon options could make the game think you're in a relationship with them. The other way is the pick either Kaidan or Ashley and then leave them to die on Virmire.