You could get a Otto Link... but in my opinion, while it's the most popular mouthpiece out there - good, yes - I don't feel it's fair to say it's best mouthpiece out there because it's the most popular, again in my personal own opinion. And from what I understand (as other people mentioned) there are a lot of Otto Links out there that need to get worked on and tweaked by a mouthpiece maker/tech to make the mouthpiece sound better.
So aside from the otto link mouthpiece...
If you want that softer, mellow sound, you want a mouthpieces with a larger chamber and lower baffle (or no baffle), maybe something with a large bore. If you want it to sound extra clear, then get a narrower tip opening (under .115 thousandths of an inch). If you want a more open, sound that might tend to be "airy", then get a wider tip opening (over .115 thousandths of an inch).
Also,
don't get the cheapest mouthpiece you can find. And if you can, buy directly from the mouthpiece maker or company, not from a middle man like woodwinds and brasswinds-- I just don't trust the "middlemen" sometimes or the quality of products that get shipped to them to get distributed to people like you and me. Usually when you can talk directly on the phone to the mouthpiece maker who's gonna make your mouthpiece, you'll end up with a better sounding mouthpiece... at least that's my experience.
So my tenor sax metal mouthpiece recommendations for a softer, mellower, and perhaps rounder sound are as follows (with convenient links to view the mouthpieces online). I'm gonna list the mouthpiece company or maker and then the specific model mouthpiece for you to look into and consider:
Sr Technologies: "The Tenor Legend" OR "The Tenor Pro 115" http://www.srtechnologies.com/products_tenor.html
Sugal Mouthpieces: "Super Gonz 1" http://www.gis.net/~schwartz/gisup/suguid2.htm
Peter Ponzol mouthpieces: "The new vintage model" http://peterponzol.com/mouthpiece_info/Pictures_of_mouthpieces/vintage_tenor.htm
Jody Jazz mouthpieces: "DV NY tenor" http://www.jodyjazz.com/dvny.tenor.html
Phil Barone mouthpieces: "New York" http://www.philbarone.com/mouthpieces/tenor/newyork.html
Runyon mouthpieces: "Smooth Bore" (without the spoiler) http://www.runyonproducts.com/smoothbore.tenor.html
Brancher mouthpieces (france): "J Chamber" (gold plated) http://www.brancher-france.com/mouthp2.htm
Theo Wanne: "Gaia", "Amma", or "Ambika" http://www.theowanne.com/Compare-Pro_Line.php
**my top 2 favorite mouthpieces are the Brancher mouthpiece and the Sugal Mouthpiece, only because I've personally owned and currently play them. I know a couple pro players who endorse Jody Jazz mouthpieces and they like them, so that would be my 3rd recommendation to look into, but look into Sugal mouthpieces or brancher mouthpieces first if you can afford them and give the guys a call and get a price quote from them!!**
You can also experiment with getting a different sax neck. Like getting a neck that is made of solid silver, copper, or bronze as opposed to having a brass neck. I got a silver neck for my unlacquered sax and it smoothed and mellowed the sound out a tiny bit and took some "brassiness" out of the sound. A copper sax neck will "fatten" and spread the sound, giving it a thicker sound with more bottom end and a better dynamic range in timbre (from a soft, round sound to a biting sound). A bronze neck might brighten up your sound and make it more focused and projected. So this is one more thing to consider if you feel like it...
As far as your embouchure... 3-6 months should be enough, if you spend lots of time listening very closely to other sax players and doing 15-20 minutes a day of dynamic longtones (with crescendos and decrescendos), tonguing exercises, overtones, deep breathing exercises, intervallic tuning exercises, and singing the intervals and scales before playing them to develop your "inner ear" in terms of timbre and pitch conceptualization-- the inner ear stuff is a big part that a lot of pros don't do much (the top pro sax players have developed their inner ear and can usually sing pitches or at least hear the sax tone and pitch in their head). If you work on these things, you'll advance quicker in my opinion.
Good luck!!