From
http://copperbadge.dreamwidth.org/693410.html -
"One presumes the Holmes Boys come from money, but it's difficult to know for sure."From the level of education and the attitudes evinced by Mr Holmes in
"A Study in Scarlet", I'd put him at the upper levels of the middle classes at the very least, but more likely a younger son of an aristocratic family whose relations don't want the inconvenience of dealing with him at home (in an earlier era, young Sherlock would most likely have been sent out of "colonial experience" to one of the colonies - either Australia or Canada would have been good candidates). He doesn't have the right sorts of attitudes to be believable as someone from a lower strata of society, and (the kicker) he's too highly educated to be believable as someone from any stratum below the upper middle classes. University education only really became available to the lower classes in the late 20th century, and Sherlock Holmes is a product of the early 20th century at best.
Some of the cues for this: he picks and chooses his case load, rather than taking whatever comes up. This is not the behaviour of someone who is doing this because they need to earn a living. It's the behaviour of someone who is amusing themselves. He spends large amounts of time experimenting - again, amusing himself. He's odd in his personal habits to the point of eccentricity, something which would most likely have had him locked up in an insane asylum (or at the very least, being kicked out onto the street by his landlady) had he not got the backing to support them. He certainly appears to have a nigh-unlimited budget for transport and travel, as well as the sorts of connections which get him in at all levels of society (read these connections, and the ones with the aristocracy are at a level of equality; the ones with the lower classes all have that element of "young master" in them).
Needing to split the rent with Watson is just a reflection of lousy day-to-day money-management skills, something you're likely to come by if money isn't something you've had to think about all your life. If it's literally been Someone Else's Problem, then you don't need to learn about it yourself.
Mycroft Holmes working as a public servant is still workable if you take the position that they're part of an aristocratic family. The tradition for aristocratic sons was to have one son who was the heir, then the others were sent to the army, the church, or the government if they wanted to be productive. So if we posit an aristocratic family with a minimum of three sons, there's the eldest who inherits the estates (and possibly a title, thus distancing himself from his brothers who wear the family name), Mycroft who has gone into government service, and Sherlock, who didn't want any of the defined social roles and instead chose to be an eccentric wastrel in the eyes of his Family.