Choosing an extension length is easy if you start from your existing bike set up. Decide if you need the same or a slightly different amount of reach and then measure from the saddle tip forward on your new frame to work out the length required.
Handlebar width and shape is more of a personal 'feel'. The modern super shallow bar shape allows a lower extension clamping height while still leaving the drops within reach.
Bar diameters must be compatible. Until the advert of over-sized bars the usual road diameter was 25.8mm (Often quoted as 26.0mm which amounts to the same thing) Cinelli were the exception at 26.2mm which didn't fit anybody else.
Older and bargain basement MTB's and a few utility road bikes use 25.4mm.
Now there are the over-size diameters: The commonest is 31.7mm but 35mm is also used by Deda amongst other brands.