If you compare the specifications for the three models you mentioned, the PSR-E303 comes out the clear winner:
Keyboard Model .... Polyphony ... Voices ... Accompaniments
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Casio LK-100 ...... 12 notes .... 100 ...... 50
Yamaha PSR-175 .... 16 notes .... 100 ...... 100
Yamaha PSR-E303 ... 32 notes .... 482 ...... 106
Obviously, there are more specifications that aren't listed above, but polyphony, voices (or tones), and accompaniments (styles or rhythms) are the most basic ones. You might want to consider other specifications if they're especially important to you, or ignore any you don't care about-- e.g., perhaps the number of accompaniments doesn't matter very much to you-- but it's good to start with the basics.
One thing you might want to consider is whether or not there might be any problems using it with a computer. The PSR-E303 has MIDI In and MIDI Out ports, so you'll need to use a MIDI-to-USB adapter or something similar to connect it to a computer. A keyboard with a USB-to-Host port would be easier to connect to a computer, but there could be issues with USB-MIDI driver compatibility, so that's something else to be aware of.