One other thing to note about pins is if you use i2c for the display, it will use pins A4 and A5. This will reduce the number of analog pins to 4.
However, i2c is a shared bus protocol, and you can hook various slave devices to the bus, including devices that give you more digital inputs or outputs, such as the MCP23017: MCP23017 - i2c 16 input/output port expander : ID 732 : $6.95 : Adafruit Industries, Unique & fun DIY electronics and kits.
If you need more analog inputs, there are i2c devices for that as well, such as the ADS1015: ADS1015 12-Bit ADC - 4 Channel with Programmable Gain Amplifier [STEMMA QT / Qwiic] : ID 1083 : $9.95 : Adafruit Industries, Unique & fun DIY electronics and kits or the ADS1115, which gives more precision to the analog values, while ADS1015 gives the same precision as the uno: ADS1115 16-Bit ADC - 4 Channel with Programmable Gain Amplifier [STEMMA QT / Qwiic] : ID 1085 : $14.95 : Adafruit Industries, Unique & fun DIY electronics and kits.
On the other hand, it is a lot simpler if you don't have to add extra chips, and you just have more pins. The Mega has lots more pins, and is perhaps the simplest solution. It has 53 pins for digital input/outputs and 16 analog input pins (which might be used for digital input/output, depending on the chip).
You could do it with the Teensy 3.1 (my microprocessor of choice), but having to switch from 5v to 3.3v might be a problem.