Analog connection only requires one connection for the signal. The signal could be a voltage or a frequency. This kind of connection is often prone to interferences if the sensor is far away from the MCU or if two sensors have close cables. So digital connection is preferred.
Parallel is not widely used as it uses 8 or 16 connections in parallel, plus additional connections for control. Main benefit is speed that fits screens and cameras well.
Serial connection is a very easy to use interface. Standard configuration is 9600 8N1, 9600 bauds, 8 bis, no parity, one bit stop. Speed can be really fast at 115200bps, about 11 KB per second. Each serial device requires a specific dedicated serial port.
SPI is a serial bus with three connections, one for clock, two for data plus an optional chip select active low. The bus consists on a master and different slaves. Data goes on two different connection, MISO or master in slave out, MOSI or data master out slave in. In case of multiple devices attached to the same bus, each device requires a chip select connection: the master select one specific device by setting the chip select low. Common speeds go up to 8 MHz.
I²C bus only requires two connections, one for clock and another for data, for many different peripherals attached to that bus. Each peripheral has its own address and the master calls each slave using that address. Standard speed is 100 kHz and the bus can include about 100 different devices, the addresses ranging from 0x08 to 0x7f.
Other standards exist but I haven't explored them already!
The most useful tools include:
A multi-meter measures analog values.
Digital connections may require logic level converters if the sensor and the MCU operate at different voltage levels.