With the regulator - for recreational diving then pretty much any currently available regulator will do - the differences are down to personal budget and preference - for example, do you want the compact second stage, myflex hoses, extra ports for extra hoses or transmitters and so on. For basic recreational diving up to 30m / 100ft then balanced or unbalanced doesn't really matter for diving purposes - as an instructor I prefer balanced but they are a little more complex and therefore more expensive to service - again, speak as an instructor I can service my own so it's not a big deal but it's a consideration for recreational divers who are not able to do this. If you're financially comfortable then it's up to you how far up the ladder you move from 'basic'.
As for the nitrox compatible or not - as others have mentioned, for recreational nitrox up to 40%, all regulators are compatible, but over 40% (the preserve of technical diving) then yes, special parts and materials are required. The only difficulty I could see with a regulator that is listed as not nitrox compatible would be some uppity dive centre somewhere who won't give you nitrox because it's not listed in the manufacturer's specification and therefore some sort of liability issue. I've never encountered this anywhere I've worked.
As for the BCD - yes - I would look at getting some training/experience/further knowledge about buoyancy but in terms of the BCD - you're a small person and whatever you buy will support you in the water. I weigh around 80kgs/175lbs and for years dived with a size small BCD, even though for regular clothes I am L - XL. And there is my point - BCDs do not come ins standard sizes. Some will take into account the use of thick wetsuits or drysuits and therefore a Large BCD designed to be worn with a thick suit might be way too big if you're diving in a rash vest and shorty - and yes, that includes adjustment. I would guess that the XS size would fit you but that is only a guess and my very strong recommendation is that you try on a particular brand of BCD before buying, or get a recommendation from somebody who is experienced enough with the product to say that yes, this will fit you. Regulators from the internet, yes, because one size fits all, but BCDs, wetsuits, booties, fins, masks, try before you buy unless you know that a particular product will fit you (for example, you used a rental set on holiday which was fitted correctly by your instructor and know that you require this or that size of a particular brand.)
Long answer I know.... hope it helps a little though.
Cheers