Well, you asked for critic so, here is mine...!
Bottle stoppers have no "official size and shape" however, there a few things that you may consider when making them. One of them, has been already mentioned and that is the length of the stopper to still fit in a normal fridge door however, not all open bottles need to be refrigerated...!
The second, and most crucial TO ME is, a bottle stopper should never finish in a sharp point. The fact that can seriously hurt your hand if the stopper its "hand tapped" as 99.9% of people do when, inserting a bottle stopper that they want to seal properly.
Apart from that, your imagination is the limit...!
I have recently (yesterday) shown here, 2 stoppers that I've done, without any consideration to if will fit in a fridge or not, when in use. They are also a lot wider at the base than most stoppers but, that was the way I wanted them to look so, and apart from the fact that, you could do a better finish in that lovely piece of wood, if you had finer sand paper grits but that, you already know.
Good tools so help considerably so, carbide tipped tools are particularly handy with burls that are a little on the hard side of things...!
I like the shape of your stopper however, I would be a little concerned with the thickness of the top "cone" at the base joint, particularly on burls that have grain all over the place and flaws/crevasses that can easily compromise its strength so, may be an issue and may not be...!
I also thing that, for someone that has never turned before, you're certainly are a courageous bloke by attempting such a shape so, 10 points to you for that...!
Keep up the good work and good luck with the purchase of those new tools...!
Cheers
George
