The decision about what tank to buy is made by considering a number of factors:
a) Capacity
b) Bouyancy characteristics
c) Longevity
d) Cost
I listed capacity first, but it's probably the most potentially misleading. New divers often want to buy much more capacity, because their gas consumption is high, but it's quite possible to end up with a tank you don't like diving at all in the search for MORE. One of my dive buddies did this -- He bought a large steel tank that was incredibly negative, and he could not adjust his trim to horizontal while using it. It was eventually sold. Most people would advise to buy a tank of reasonable size and better buoyancy characteristics, and accept that one's dives will be shorter than ideal until one's gas consumption falls with experience and better technique.
What is acceptable or desirable in terms of buoyancy depends greatly on where one is diving, and what exposure protection is being used. When I dive in the tropics, an Al80 is entirely acceptable to me. It requires about six pounds of weight, which is something I'm willing to carry, and CAN carry in such a way as to be able to maintain horizontal trim. In Puget Sound, in a drysuit, I have to carry 38 pounds to sink an Al80, and that's more than I'm willing to do, and more than I can easily distribute correctly. If I dove fresh warm water, the steel tanks I dive in Seattle would most likely be too negative, so that I could not achieve the state of being neutral at the surface with 500 psi and an empty wing.
The physical size of tanks can become quite important when you dive doubles, but I don't think that's nearly the issue with a single tank.
Steel has a much longer life than Aluminum, but unless you are sure you're going to be diving for 30 years, that's probably not a high priority consideration.
Steel tanks are considerably more expensive than aluminum, which can be a significant factor for new divers, who are in the process of laying out the considerable amounts of money required to get into their own gear.
Putting weight on your back will not make you unstable or make it harder to swim. It may well make it EASIER, in that you will find you tend to be more horizontal. However, if the tank you select is too large and too negative (big Fabers) you may end up with the opposite problem, being head heavy. (This is what happened to my friend.)