If I violated probation for the first time, what would be the outcome for me if I turn myself in?

It always helps if you turn yourself in, rather than running.  But as far as the actual outcome-- that will depend on the nature of your violation, the level of the offense that you are on probation for, and the disposition of your judge. 

Lower level violations, like failing to pay all of your fine or court costs often result in reinstatement of a defendant's probation, with possibly an extension of their probation to give the defendant additional time to meet the financial obligation.  Failure to follow the general rules of probation are referred to by many judges as "technical violations," and are treated much more lightly.  If you have a probation violation because of a new offense and you are guilty of that offense, then there is a fairly good chance that your probation will be revoked and you could be sentenced to a period of confinement in the county jail or state prison (depending on the level of your offense.)

The level of your offense can also affect what the judge can and cannot do.  For example, if you are on probation for a misdemeanor level offense, you can only be sentenced to time in the county jail, not the state prison.  If you are on deferred adjudication for a state jail felony drug possession charge, then the judge has a mandatory requirement to place you on a strait probation-- which also means that you cannot be sent to the state prison.

In the end, however, what will happen will depend on your judge.  Some judges are very defense oriented and work hard to offer defendants mulitple opportunities at rehabilitation before they finally revoke their probation.  Other judges are very "by the book" and expect strick compliance with the rules of probation-- these judges are more likely to revoke and send a defendant to prison.  No attorney can guarantee what the judge will or will not do, but to get a better idea of your judge's feelings about motions to revoke, arrange for a consultation with at least three defense attorneys.  It is inconvient to have this many meetings, but it will give you a good survey of how your judge tends to rule.