Trek and Specialized are both reputable mfrs that make a variety of bikes in all styles (mountain to time trialing and everything in between) and price ranges (from not too unreasonable to absolutely ridiculous). I have a Trek road bike and a Specialized mtn bike and enjoy riding both of them. And there are other good brands as well.
An issue that the LBS guy may be trying to alert you to is that it's really easy to start upgrading an existing bike and adding accessories, etc to the point where you have invested more $$ than a new, better bike would have cost. A new saddle could be important to your riding comfort and essential for you to put in more miles and meet your fitness goals, however.
You might want to continue riding your existing bike for a while until you've pretty much done as much with it as you can and have lost some more weight. Then consider what you want to do with cycling and buy a new, better bike that is designed for your particular wants and needs.