I would guess the traditional choice would be 750ml corked bottles. Colored bottles if you think you have ingredients that would be light struck (flavor changes due to sunlight shining in the bottles). Otherwise, clear is a nice choice as you can see the wonderful color of mead. Style of bottle - I am not aware of any traditional bottle style used for mead so I go with what I like.
I notice a lot of Meaderies going to 500ml bottles. The thing that used to get me about bottling beer in 12 or 16 oz bottles was having to have 'Many Cases' of bottles per batch, and that traditional beer caps were not reusable (bottling a big batch took significant time).
I have found that I am using a lot more 375ml bottles (half bottles). They seem to be a nice size for folks who want to try mead but don't necessarily want to start with a full bottle. (I note that a lot of 500ml bottles sell in the $20 range - some folks might risk $20 on trying something new, but might not risk $30 for a larger (750ml) bottle. (There is probably a whole marketing/price/value/perception discussion here - but it does not apply to me.))
Corks are probably the most used closure. Swing Top or Bail (Bale) bottles with rubber sealing rings are also popular. Bottle caps work well, but not resealable (I suppose you could say the same for corks.) Zorks are re-closable, look cool, but are too expensive for my home-brew non-commercial operation.
I personally have gone to screw top bottles with good poly-seal caps. It means I am buying bottles (and caps). But, bottling is easy regardless of bottle size, resealable, and I have found the caps can be put on just tight enough to allow any pressure buildup to escape but not allow air in. Getting the empty bottles back from friends is a bit sporadic, and a few of each case just go missing, so I have a constant investment. This probably also applies to Swing Top bottles.
For me, a big deal is a label. It just seems to finish the bottle and set it apart from un-lableled bottles. I usually put a title and picture on the front, and some trivia about the variety, honey used, adjuncts, historical facts, etc., on the back. I print them on regular paper and stick them on with a 50/50 mixture of water and milk. Keeps the label on, but it comes off easily when the bottle is washed. (Since I am not a commercial operation, I don't need all the warnings/approvals.)
Advice from this forum has allowed me to really step up my game and make mead that has people saying, 'Wow. This is good stuff.'