Most small microcontrollers will be capable of doing what you need. You could even ditch the Arduino "wrapper" and use a USB capable micro in it's place.
Microchip, Atmel, TI, ST, etc all have 8, 16, 32-bit uCs of varying RAM/FLASH/EEPROM sizes to pick from. All the modern uCs come with at least UART, SPI, I2C peripherals that can be used for your communications.
There is not a lot in them really, I'd just pick one and see how you like it.
I (currently) use ST's 32-bit ARMs and Microchip 8, 16 ,32-bit PICs.
I'd probably use a few PIC12F or 16Fs for the slave uCs and a PIC18F or PIC24F for the master.
You mention needing ~10kbits of memory (not quite clear what type or which uC needs it from your description to me though)
It's easy to determine what is suitable though, just check the RAM/ROM/EEPROM specs of each uC you look at.
For example the PIC16F1938 has:
Parameter Name Value
Program Memory Type Flash
Program Memory (KB) 28
CPU Speed (MIPS) 8
RAM Bytes 1,024
Data EEPROM (bytes) 256
So 28KB of program memory is more than enough to store non-volatile data if your program is small enough (on the newer PICs you can also read/write to program memory at run time) 10kbits will not quite fit into the RAM though, at 1024 * 8 = 8192 bits.
The 16F1527 has 1536 bytes of RAM though, so you could use this if necessary.
For the master (alternatives to Arduino) there is something like the 18F25J50 or similar, which has a USB 2.0 peripheral. Microchip provide a USB stack an plenty of example firmware to get you started with USB.
If you need something more powerful for the master, have a look at the PIC24 series with up to 256K of Flash and 96K of RAM. Or even the PIC32 which is 32-bit and up to 80MIPS.
The PICKit3 is a low price programmer that will program all the above mentioned PICs, and MPLAB (or MPLABX) is a free IDE for firmware development.
Communication can be done with I2C, which deals with the master/slave configuration and addressing easily. All you have to worry about is sending the data. 7 meters should be no problem with a reasonably quiet environment and the right setup (low value pullups - say 2.2k, low capacitance cable)
You can build a simple RC5 decoder using a PIC microcontroller.
Transmitter:
Use a universal remote with Phillips TV settings. RC5 is a protocol designed by Phillips for their TV, VCR, etc remote controls. By using RC5 protocol, you eliminate the need to design your transmitter. Just use any universal remote control and program it for Phillips TV. I have seen universal remotes floating at 99-cents only stores in Southern CA.
Receiver:
A RC5 decoder can be built around a PIC microcontrooler. Take a look at RC5 Decoder with PIC Microcontroller. This article describes RC5 protocol, hardware and software needed to decode RC5. You many have to change the code to your taste. To drive motors, use simple transistor drivers at PIC outputs. The motor driver depends on the type of motor you are using.
Best Answer
You likely want something like a Tag-Connect:
They're available in 6 and 10 pin versions, with and without the plastic retaining clips. You can find them at places like Digikey. They are not cheap ($35), but you'd only need to buy a couple to program a ton of boards.
As a side note: I think when you say "jumpers" you really mean "headers". Headers are the pins, jumpers are usually blocks that short pairs of those pins.