Since I think BrettAM already gave a pretty good answer, I'm going to expound just a little upon that.
First off: I think you're misunderstanding sample rate. The sample rate here is simply the number of analog readings per second that you are doing of a given signal.
If you want to know the maximum sample rate of the Arduino, you simply have to take a ton of samples as fast as you can and see how many you were able to take in a given second. For the Arduino with default settings, that's ~9600 per second maximum. If you just take 1 single sample though, your sample rate is......I don't know.....how often do you do this!? If you take 1 sample and then stop your sketch for an hour, your sample rate for that one sample was 1 sample per hour. Now, what are you sampling? If what your're sampling is changing faster than one noticeable change (ADC resolution step) per hour, then you need to sample faster than once per hour. If your signal (what you're sampling) is changing at 100 times per second (100Hz), however, then you need to sample at at least 200 Hz to even detect it's changing at 100Hz, and at approximately 1000Hz or higher to actually plot what that 100Hz signal looks like. Note: sampling at 2x the rate of the sampled signal is the minimum sample rate required to detect the frequency of the sampled signal, and is called the Nyquist Frequency. Sampling at 10x the sampled signal is the generally-accepted rule-of-thumb for minimum sample rate required to capture the waveform, or shape of the sampled signal.
Now, let's look into data smoothing. If you just take a single sample, it might bounce around. How do you stop this? One method, is to take many samples and average the result. A library I wrote does this, among many other things, so I'll present it here.
Taking many samples in a row then using the average of the samples in any calculations helps to remove the noise component from your signal. I have written an oversampling library that among other things, does just that. An (outdated..will be updated eventually) page on it is here: Using the Arduino Uno’s built-in 10-bit to 21-bit ADC (Analog to Digital Converter).
The current version of the code is V2.1 alpha, and the download link is currently highlighted in yellow at the link above.
In case you need to take faster samples, you can also speed up the ADC sample rate to 50+ kHz, using my library...as opposed to settling on the default 9600Hz of the Arduino.
Play around with sampling and smoothing and stuff. One technique is to speed up the ADC (so you don't waste too much time sampling), then take the avg. of many samples in order to help remove noise from your sensors. This may be unnecessary, if noise is minimal or changes over time on the signal are slow, but for the sake of learning I'll present this.
Here's an example sketch:
//include the library
byte pin = A0;
byte bitsOfResolution = 10; //commanded oversampled resolution
unsigned long numSamplesToAvg = 50; //number of samples AT THE OVERSAMPLED RESOLUTION that you want to take and average
//Configure the adc how you want it
adc.setADCSpeed(ADC_PRESCALER_16_CLOCK_1MHZ); //this speeds up the ADC clock by a factor of 8
unsigned long analogReading;
//take a reading on the analog pin
analogReading = adc.newAnalogRead(pin,bitsOfResolution,numSamplesToAvg);
You'll see that I am speeding up the ADC and taking and averaging 50 samples to smooth the data. I have yet to test the speed, but I estimate this could prob. run at 500Hz or so max sample rate (returning an average value each time)...assuming that's all you did.
Doing this and taking a single sample is fine for what you need I believe.
Now, for baud rate. Baud rate is essentially "bits of data sent per second." It's how fast your communication signal is. Lower baud rates are generally less susceptible to electrical noise, and the data is less likely to get corrupted, but higher baud rates send the data values much more quickly and waste less of your code time sitting around transferring data. I recommend you speed it up to maximum, unless you have data transfer problems or dropouts, in which case you should slow it down a bit.
NOTE: for more detailed examples on the library download it and look in the examples folder.