The INA125P is an amplifier, capable of amplifying a signal up to 10,000x. It will work with a load cell but without an accompanying analog-to-digital converter (ADC) you'll be stuck with the Arduino's 10bits of precision (1024 measurement points).
The MCP3551 is an ADC converter with 22bits of precision (4,194,304 measurement points).
The ADS1231 is an amplifier (127x gain only) and a 24bit ADC.
So you could use the INA125P alone but you wouldn't have many measurement points. If you used the MCP3551 alone you'd have a lot of measurement points, but the signal would be small and you'd only use a fraction of them. So an INA125P and a MCP3551 together would work great, or you could use the ADS1231 and get (essentially) both in the same package.
The Chinese HX711 (check eBay/google) is comparable to the ADS1231. Since you can get it on a pre-built module (and cheap) it would be the easiest one to get started with.