Does the performance of a symmetric encryption algorithm depend on the amount of data being encrypted? Suppose I have about 1000 bytes I need to send over the network rapidly, is it better to encrypt 50 bytes of data 20 times, or 1000 bytes at once? Which will be faster? Does it depend on the algorithm used? If so, what's the highest performing, most secure algorithm for amounts of data under 512 bytes?
Obviously, performance depends on the amount of data as every part of the data has to be encrypted. You'll get much better information by doing a test in your specific environment (language, platform, encryption algorithm implementation) than anyone here could possibly provide out of the blue: I don't think it would take more than half an hour to set up a basic performance measurement.
As for security, you should be fine with Triple DES or AES.
Symmetric encryption algorithms typically are block ciphers. For any given algorithm, the block size is fixed. Then you pick from several different methods of making subsequent blocks dependent on earlier blocks (i.e. cipher block chaining) to create a stream cipher. But the stream cipher invariably caches incoming data and submits it to the block cipher in full blocks.
So by doing 50 bytes 20 times, all you're doing is pounding on your cache logic.
If you're not operating in stream mode, then datagrams smaller than the native block size of your cipher will get significantly less protection than complete blocks, since there are fewer possible messages for an attacker to consider.
AES should be a good choice.
Good implementations of AES (e.g. the one included in the openssl library) require about 10-20 CPU cycles per byte to encrypt. When you encrypt small messages then you also have to consider the time for the key setup. E.g., a typical implementation of DES requires a few thousand cycles for a key setup. I.e., you might actually finish encrypting a small message with AES before you even start encrypting with other ciphers.
Newer processors (e.g. Westmere based CPUs) have an instruction set that supports AES, allowing to encrypt at speeds of 1.5-4 cycles per byte. That is almost impossible to beat by any other cipher.
If possible try encrypting longer messages, rather then splitting them into small pieces. The main reason is not encryption speed, but rather security. I.e., a secure encryption mode usually requires to use an initialization vector and a message authentication (MAC). These will add about 32 bytes to each of your ciphertext parts. I.e. if you divide your message into small parts then this overhead will be significant.
The short answers are:
You want to encrypt all your data in one go. You actually want to give them all in one function call to the encryption code, so that it can run even faster.
With a proper encryption algorithm, encryption will be substantially faster than the network itself. It takes a very bad implementation, a very old PC or a very fast network to make encryption a bottleneck.
When in doubt, use an all-made protocol such as SSL/TLS. If given the choice of the encryption algorithm within a protocol, use AES.
Now the longer answers:
There are block ciphers and stream cipher. A stream cipher begins with an initialization phase, in which the key is input in the system (often called "key schedule"), and then encrypts data bytes "on the fly". With a stream cipher, the encrypted message has the same length than the input message, and encryption time is proportional to the input message length, save for the computational cost of the key schedule. We are not talking big numbers here; key schedule time is below 1 microsecond on a not-so-new PC. Yet, for optimal performance, you want to do key schedule once, not 50 times.
Block ciphers also have a key schedule. When the key schedule has been performed, a block cipher can encrypt blocks, i.e. chunks of data of a fixed length. The block length depends on the algorithm, but it is typically 8 or 16 bytes. AES is a block cipher. In order to encrypt a "message" of arbitrary length, the block cipher must be invoked several times, and this is trickier than it seems (there are many security issues). The part which decides how those invocations are assembled together is called the chaining mode. A well-known chaining mode is called CBC. Depending on the chaining mode, there may be a need for an extra step called padding in which a few extra bytes are added to the input message, so that its length becomes compatible with the chosen chaining. Padding must be such that, upon decryption, it can be removed unambiguously. A common padding scheme is called "PKCS#5".
There is a chaining mode called "CTR" which effectively turns a block cipher into a stream cipher. It has some good points; especially, CTR mode requires no padding, and the encrypted message length will have the same length than the input message. AES with CTR mode is good. Encryption speed will be about 100 MB/s on a typical PC (e.g. a 2.4 GHz Intel Core2, using a single core).
Warning: there are issues with regards to encrypting several messages with the same key. With chaining modes, those issues hide under the name of "IV" (as "initial value"). With most chaining modes, the IV is a random value of the same size of the cipher block. The IV needs not be secret (it is often transmitted along with the encrypted message, because the decrypting party must also know it) but it must be chosen randomly and uniformly, and each message needs a new IV. Some chaining modes (e.g. CTR) can tolerate a non-uniform IV but only for the first message ever with a given key. With CBC even the first message needs a fully random IV. If this paragraph does not make full sense to you, then, please, do not try to design an encryption protocol, it is more complex than you imagine. Instead, use an already specified protocol, such as SSL (for an encryption tunnel) or CMS (for encrypted messages). Development of such protocols was a long and painful history of attacks and countermeasures, with much grinding of teeth. Do not reenact that history...
Warning 2: if you use encryption, then you are worrying about security: there may be adverse entities bent on attacking your system. Most of the time, simple encryption will not fully deter them; by itself, (properly applied) encryption defeats only passive attackers, those who observe transmitted bytes but do not alter them. A generic attacker is also active, i.e. he removes some data bytes, moves and duplicates other, or adds extra bytes of his own designing. To defeat active attackers you need more than encryption, you also need integrity checks. There again, protocols such as SSL and CMS already take care of the details.