Ultrasonic rangefinder (for beginner)
1 . Breadboard or Stripboard will be fine for prototyping/learning purposes. FOr the latter you need to have basic skills with a soldering iron.


Either should be fine for basic distance sensing. You have more control with separate units , for instance if you want the receiver and transmitter to have different polar patterns (sensitivity angle - you could put one in a tube to make it more directional for example) or slightly different angles (for whatever reason)  
Can be powered by any reasonably clean ~5-12VDC >250mA supply (probably get away with less but 250mA is easy and makes sure you have plenty for additional stuff like LEDs, LCD, etc) This could be a DC wall brick, batteries, etc. You will need a regulator (e.g. 3.3V LDO) for your micro but the transducers can be powered directly (up to 20V rms according to Velleman page)
You will need a couple of general purpose transistors (NPN or N-ch MOSFET - BC337-40 is a good choice) to switch the transmitter with, as you will want to use the higher voltage input rail (rather than the regulated micro rail) for extra range. 
Any small 8-bit micro with a couple of timers, a PWM peripheral (a comparator/ADC would be nice) will do for simple sensing and display on e.g. LCD. This could be a PIC16F, PIC18F, AVR of some sort, MSP430, etc. You can get simple dev boards or "starter packs" for all these micros that will get you up and running quickly. For example with a PIC16F you can use MPLAB/MPLABX to write your code on, and use a PICkit3 to program the chip with. Here is an 18F pack that includes dev board and PICkit3. Lots more boards here.
I assume you mean using Proteus for development (I have only seen it's PCB design part) This is okay if you want to go that way, Proteus has a pretty good rep from what I have heard. Personally though, I would stick with the tools provided by the people who make the chips (unless they don't provide anything) I have used MPLAB for all my PIC development and it's a very solid platform. MPLABX is the next generation IDE, based on Netbeans.