As a footnote to my previous posting, a lot of the incentive to try different mouthpieces was that my practice room is my caravan, where the acoustics are not merely dead but have been mummified and buried. Until I got to the Rico mps my tone sounded to me like a bee in a bottle. The bright tone of the Metalite finally enabled me to overcome this and produce a sound which reminded me of a saxophone.
The net result of this is that when I play anywhere with average acoustics and start straight off emoting through my sax and giving it welly I sound like a tenor-playing poor man's version of Ornette Coleman having a nervous breakdown.... which is fine, because what I tend to do is start with something cool and restrained and get the feel of the acoustics before letting rip and risking triggering audience anxiety attacks, collective outpourings of grief and mass suicides. After a week getting used to it I found could peel paint or play lullabies with the Metalite at whim, so it is not a problem.
There a number of thoughts here.
How you sound to yourself is not how others hear you - this pops up every now and again on this forum.
If you can, try your sound in different rooms if only to assure yourself that you can actually make something like the sort of sounds you are aiming for. It also alerts you to the tremendous variation you will find in venues if you get to play in public.
Provided that it doesn't depress you too much and make you want to give up, very dead acoustics will make you work like mad on producing an expressive sound. It also encourages you to practice playing loudly - but which doesn't prevent you from playing at low volume when required...
Outdoor acoustics can be very 'empty' (e.g. in a field) and very off putting if you are not used to it, too.
Contrariwise, if you regularly practice somewhere with a nice bit of natural reverb then if you have to play somewhere with dead acoustics you will lack confidence and really struggle. You will also probably lack practice at playing loudly with a good tone and for long periods, which isn't at all good if you really need to and can't...
None of this is a recommendation for buying mp after mp in the hope of getting a better sound... whichever of my mps I play on, I sound like me - but a quieter and more subdued me on the first couple .... and I can do much more, and do it better, with my current favourite.
But until your embouchure is well developed, a conservative, middle of the road student mouthpiece is worth sticking with. I moved from one to the next quite quickly because I had played years before, and just needed to get my chops back in shape and knew more or less what I was looking for.
Chopping and changing frequently is not a good idea for a beginner, and a mp which suits a more experienced player may be hard to play well if your embouchure and experience is not ready for it.