Summarize:

If you're just starting out with the instrument, there's no need to spend an excessive amount of money on a violin, but like most instruments, the quality of the violin generally rises as the price goes up. Expect to spend a few hundred dollars on a decent beginner's violin.  Buy full size or 4/4, if you're an adult. The violin is a small instrument, but there are specially designed smaller sizes available. These are generally only intended for younger children, so be sure the violin you're buying is full size unless you're very small. You can ask the shop for a recommendation if you aren't sure.  You can also ask the shop to measure your arm length to see what size violin you need. When holding the violin in the playing position, straighten your left arm and the tops of your fingertips should be near the top the violin scroll. If your arm is way past the top, the violin is too small. Buy from a reputable seller. Music stores stake their reputations on selling solid instruments that are free of obvious flaws and damage. As a beginner, you won't be able to coax a very pleasant sound from your instrument for some time, so flaws in privately sold violins might not be apparent to you until it is far too late to complain. Only buy from a store or individual you can trust. Unless you have purchased the instrument only, your violin outfit should come with a violin with four strings, a bow, and a carrying case and most of the time a chin rest and rosin for your bow. In most cases, the person who sells you the violin will be happy to string it for you, which has the added bonus of double-checking to be sure the tuning pegs (the knobs at the scroll, or top, of the violin) are properly fit to the scroll. A hard case is important because violins are such delicate instruments.  Strings come in three basic varieties: gut, which is expensive and difficult to take care of, but which offers a complex range of sound; steel, which is loud and bright but can sound scratchy, and synthetic, which is smooth, clear, and not as unpredictable as gut. Each type's name refers to the core material around which metal wire is wrapped to create the string. Most beginners should go with synthetic core strings, such as nylon core.  The bow should be new, or newly re-haired. You can check this by looking at the hair of the bow (the fine, white or off-white fibers) and ensuring that the color is uniform and bright along its entire length. The hair of the bow should be a uniform width from end to end. Bows wear down over time. You can get your bow re-haired for a small fee at most music shops. Nearly all violinists use a chin rest, which is a cheap, ergonomic piece of (usually black) plastic that clamps near the base of the violin and allows it to be held securely by your chin. This is usually attached to the violin when the violin is built. Aside from that, be sure you have some rosin (coagulated sap) for your bow, a music stand, and a book of beginner lessons or songs, preferably in a format that will open flat.  Some violinists, especially beginners, also purchase a shoulder rest, which is a violin-width pad that sits on your shoulder underneath the violin and makes it easier to hold. Many people start with a shoulder rest and eventually remove it after a few years. If the violin seems to dig into your shoulder when you play, consider purchasing one. Fiddlers, if they sing while performing, often hold the violin in the crook of an arm while playing, with the butt resting against their shoulder. For them, chin rests and shoulder rests are generally pointless. A tuner is a small device that clips on to the scroll or the pegs of the violin. It is useful for beginners if you are teaching yourself, as it can be used to make sure you are playing the notes correctly. But once you know how to play the notes, the tuner isn't of much use anymore except for tuning the instrument itself. Be sure to take it off before big performances though, as it looks unprofessional.
Buy or rent a violin. Check the accessories. Purchase other items.