A type rating with no flight hours in that plane looks unusual and is a waste of time (except for SWA, as I understand). It doesn't matter if you show up on day one with a 757 type rating, the company will not assign you to a 757 based upon that nor with you get preferential treatment in training. My training partner in the 727 FE seat was a 727 LCA from another airline and he went through the entire training program like I did. Granted, he was bored and I was just a source of his amusement as he watched me flail around on the panel in training, but they didn't put him in the 727 just because he has the rating.
A 737 type rating might cast doubt upon your intentions when you interview with either FedEx or UPS (I presume) since neither company operates the 737. You might get around that in the interview by saying something like, "...I want to leave my options open..." But if you have a 737 type rating without flying one operationally, you're leaving yourself open for the interviewer to doubt your true intentions.
The two most important things for you, have been mentioned by other posters:
1. Fly, and have recent flying experience when you interview.
2. Have people in the company you want to interview with who have flown with you and will recommend you.
This far out (and with three years remaining, yes, you are a ways out--as a previous poster noted, a lot can happen in three years in this industry), monitor the industry, track the companies you want to work for, and keep talking to your like-minded squadron-mates to discuss issues and keep up to date with what's going on in the industry.
A personal recommendation from a current pilot employee, recent flying experience and meeting the company's requirements should be your focus. Don't waste money getting a type rating you don't need and which might actually work against you in certain circumstances. If you really have that kind of money to burn, take you wife to Paris for a long weekend--that will pay bigger dividends down the road.
Best wishes.