diff bet i2c and rs232 communication
If you don't know which protocol to use, you probably don't need any, cause your application doesn't require a protocol. I wouldn't reagard RS323 or 485 as a protocol, it's a physical a physical layer used in a protocol.
I2C is a different pysical layer together with a specific protcoll, but's it's completely inappropriate for communications outside a device respectively for distances above 1 m.
Also CAN uses a specific physical layer different from RS232 or RS485, for this reason it always requires a special controller hardware.
MODBUS in contrast is protocol, that can use any RS232 or RS485 hardware, either on a PC or in an embedded processor. It also is rather simple, that's why it's popular, I think. It's a defined open standard (originated from Schneider) to pass data (single bit digital and 16 bit "analog") between one master (or client) and many slave (or server)
stations. It's particular useful when you intend data transmission to or from devices from different vendors.
When you don't need to be compatible to any existing standard, you not necessarily need a complete protocol, just a definition, in which format you transmit data. You could e. g. print measurements in text format to a serial line, in a format that could be displayed on hyperterminal for a human reader or printed to line printer. But it may be read and interpreted by a computer as well. A lot of devices sending data on an interface work this way.