The PIC24FJ64GB004 is also available in TQFP package, and that is what is used on the plug-in module for the Explorer 16 motherboard.
If you don't need all the facilities of the Explorer 16 motherboard, you could just buy the module (part number MA240019) and make your own motherboard to your requirements. The Explorer 16 board does not come with the chip you want - it comes with a module for the PIC24FJ64GA004. So you would have to buy the extra module anyway.
The explorer board needs a programmer, unless you buy the Explorer 16 Starter Kit full package which is even more money.
For programming it, you could use a PICKIT 2 with the separate (free) programming application, but there will be no debugging support because Microchip hasn't added support for that in MPLAB (they would rather you buy the newer PICKIT 3 of course). Or, I think an ICD-2 (again, the older version of the ICD) is supported in MPLAB with this chip with debugging support. Both of these programmers can be had as cheap-ish clones on ebay, or sometimes as second hand real ones.
Personally though, if you are likely to do anything else with PICs, I would recommend buying a PICKIT 3.