Hi,
what is the difference between a 1k thermistor and a 10k thermistor?
The resistance obviously

Does the 10k have more precision or something?
Nope.
whats the difference between the various types of thermistors? I have one thats labeled 'bead' another thats labeled 'disk' and another that isnt labeled but looks weird.. i also saw some that look like a disc capacitor.
Bead thermistors are shaped like, well, small beads and disks are... You guessed it - Disc shaped.
The smaller the physical size (mass), the faster it reacts and v.v.
Some are like the head of a pin for fast reaction (used on eg. the early variety of "instant" body thermometers). Some are integrated into various shapes of bolts and tubes etc. it's a matter of adapting shape to purpose.
attached are some pictures of the ones i have.
Ahemmm?
You can use either of the ones you have for the schematic you linked to, just use a resistor of the same value in the voltage divider.
The nominal value of a thermistor is the resistance at 25°C.
NTCs are non-linear devices.
You can either use a table to correct for this response, or, if less sensitivity is OK, it can be linearized to a reasonable degree by adding a parallel resistor (which must be matched to the specific NTC and the main temperature region it's supposed to act in).
It's a bad idea to go 0°F to 250°F, as the non-linearity will be vast over such a range.
In a body thermometer for instance, you only need a range of 35°C to 42°C, making the linearity error very small.