The BA and BR are a good choice of breeds. The Wyandottes I've had in the past didn't justify their feed, nor the EEs. How many can you keep where you live? In other words, what is your goal for flock size and are you equipped to handle it?
If you can only have 6 chickens it's going to be hard to cull for hardiness and lay and still get enough eggs to be worth the trouble. Say, starting with six pullets of various egg laying breeds the first year. Come next spring you check for laying or you notice some failure to maintain weight or keep good feathering or any other health feature that is undesirable...and you have to cull a couple. Then you have to replace those but when doing your own replacements you have to have a broody(no eggs being laid by her while doing so) and they usually start going broody in early spring/summer...by the time their chicks are fully producing at peak it is next year.
Meanwhile you might have 3 chickens laying but they hit molting time and slack off, so you may be getting an egg or two a day. If that doesn't bother you, then a small flock like that is worth working on until you get the very best 6 hens you can keep and, afterwards, look forward to a few years of good laying with steady replacement chicks coming along to eat or keep. It takes time and patience, but if you start out with good breeds and go from there, it is possible.
Ideally, IMO, to have a good backyard flock that produces enough eggs to eat and sell a little to defray feed costs, one needs at least 15 hens but better if you keep 25-30. If that isn't possible and you just want eggs for consumption and you don't mind that for the cost of the feed you are buying you could probably buy eggs a lot cheaper from the farmer down the road~then 6 is a good number.
If dealing with 3 hens it isn't even worth the time to turn around...no possibility of any long range plans for a self-sustaining flock at all. Buff Orps will eat you out of house and home and become too fat for good laying qualities. This has born out each and every time I've tried to include them in any flock of mine over the years. They are also too docile and become the roo's favorite slip and slide, leaving their backs as bare as grandma's cupboard all the time.
My very fave breeds~in order~ for egg production, extreme good health, occasional broodiness but not excessively so and just plain ol' longevity of lay are these...other OTs may have additions to this list:
Black Aussies **** Can't say enough good things about this breed!*****
White Rocks****Or this one!!!*****
New Hampshires
Barred Rocks ****** Just about any of the Plymouth Rock variations are a great breed.
RIRs and Leghorns ****These two production breeds are worth keeping for as long as can to produce many eggs but don't build a whole flock around them(unless you happen upon a breeder with some good, old lines)...they are great for keeping some eggs going through the winter while the other breeds take a little break. I usually pepper a flock with 4-5 of these out of 25-30 hens. If they don't burn out and make great hens, so much the better.
Speckled Sussex
Dominiques *****Only from a good breeder of old lines...hatchery stock is none too hardy...not a bit like the Doms my granny always had****
Partridge Rocks
There are several breeds I haven't tried that I would like to eventually... all are old heritage style breeds that haven't been too eroded by hatchery breeding~Buckeyes, Barnvelder, etc..
Breeds I'll not try again:
BOs or any other variation of Orpington
Any variation of Wyandotte
Production Reds or Blacks
YMMV