It would be nice if you have a squeeze page on #1 in Google. Unfortunately Google does not like this idea so much. So you can build backlinks to it and try to rank it but it is most likely a waste of time and money.

Advertising a squeeze page: Sure, that is what you do with a squeeze page. Drive traffic to it. The more the better.

Whether it works best to advertise the squeeze page directly or whether you should send the traffic first to some content: you have to test. Depending on your niche or market the results may vary.

There's no point in backlinking a squeeze page, because they wont rank in google anyway.

So don't waste any time or money back linking a squeeze page,

As said by others above, its really not worth it to build backlinks on squeeze page and trying to rank it. rather drive targeted traffic. Things have worsen up after all the updates and google was never in a good mood to rank squeeze page anymore, as they consider it a static page. So it would be better if you drive traffic to your squeeze page through advertisement. Thats work best for everybody.