"Are most cages universal fit?"
Yes. The two screws are on standard center dimension and cages are usually slotted to allow for some adjustment and/or manufacturing tolerances.
"Are there certain brands that are better than others?"
Yes, but it comes down to a couple of characteristics:
1. Looks
2. How securely the cage needs to grip the bottle
3. Material choice.
Aluminum cages tend to mark up bottles more so than other materials. Paint and even anodizing will wear away over time/use.
Stainless steel cages may be a bit heavier, but look good for years and are generally very sturdy. Like aluminum, they can be bent to improve grip on the bottle.
Titanium cages can be an excellent choice. They offer little over aluminum or stainless, but they go well with Ti frames.
Polymers/Nylon cages are very durable as a rule, will not oxidize and come in a variety of styles such as side insert/removal of the bottle. Grip can be anywhere from poor to excellent depending on design.
Carbon fiber are usually sold for both bling factor and low weight. The can be somewhat fragile and probably suffer the highest failure rate if the internet is to be believed. Grip, again, can range from poor to really good.
I like the Elite cages. Check out the Custom Race model. It works well for me. In stainless, the King cages are very well made.