Most general contractors will be able to do plumbing, electrical, paint, carpentry, masonry, finishes, etc.
Doing it yourself usually costs more than you anticipate from a general contractor. Especially when you realize that you will be investing your time as well as your money. Plus, many subcontractors give low priority to smaller jobs and do-it-yourself jobs. You will not have to worry about being on the bottom of the list whey dealing with a general contractor. You would rather get the work done with a general contractor then extend the time of your house being built.
When you decide to hire a general contractor be careful in your selection, your home is literally in their hands.
The first thing to do when hiring a general contractor is to ask for their business license and the name of their insurance provider. Then call to verify that both are authentic. Reputable general contractors will be licensed by the state and will carry workers' compensation and property damage/liability insurance.
The general contractor should have referrals to current and past clients whose projects are comparable to yours. Visit past projects to inspect the work of the general contractor. Call suppliers and subcontractors to check that the general contractors bills have been paid on time.
Also, call the local building inspection department. Ask what they think about the general contractor's work. The building department is one of the best consumer advocates and references you can find when looking for a general contractor.
You should ask how long the contractor has been in business overall as well as under his current name. Be suspicious of contractors who've changed their letterhead often; they may be dodging their past.
Lastly, look for contractors who belong to industry associations such as the National Association of the Remodeling Industry and the National Association of Home Builders. Membership indicates a dedication to their work and an interest in keeping up on the industry.