If you decide to go with the FPGA, here is a dev board that will work for you:
https://www.eevblog.com/forum/microcontrollers/terasic-cyclone-v-gx-starter-kit-(c5g)-review/But FPGA programming is not for the faint hearted, It will literally take you at least 3 months to get your head around it, and you will learn a lot. Just connecting eclipse or whatever IDE you want to use to hook into the soft core will take a lot of research. You can use the NIOSII soft core but Altera doesn't offer it for free.
There might already be work done to connect the Arduino dev environment to the soft core but I haven't look into that.
Altera has a good guided course curriculum that will help you along, but expect to spend a lot of hours and because iteration makes for better learning you will need to revisit the courses until you know exactly what's what or at least to the degree that you don't have to go through the training tutorials.
If the GPIOs in there are not enough, then you can get this card too for more GPIO's that you can handle.
http://www.altera.com/education/training/curriculum/fpga/trn-fpga.htmlNote it does have HDMI out but you will have to learn I2C to communicate and setup the chip then drive it with a frame buffer programmed in the FPGA.
So it's doable but it's gonna require a lot of dedication and a lot of learning to get there.
Alternate to this is to grab a Pioneer board and an lcd shield, it's a 32bit Arm Cortex M0 with programmable analog and digital components. But this won't take sketches (I believe that's what programs are called on that world) It will however allow you to program in C. And tons of examples
http://www.element14.com/community/thread/23736/l/100-projects-in-100-daysAll that said, if you want 100MHz, forget the pioneer, you might get 20KHz at best.
The other one, will take a lot of coding and you will need a better ADC and ACD that the one on board. But money talks:
http://www.terasic.com.tw/cgi-bin/page/archive.pl?Language=English&CategoryNo=67&No=360&PartNo=2Two 14-bit Analog to Digital (A/D) converter channel with 150MSPS
Two 14-bit Digital to Analog (D/A) converter channel with 250MSPS
One Audio CODEC with Line-In, Line-Out, MIC and Headphone
With that you might get 50MHz using 3 samples but that would be crappy, 20MHz might be more realistic.
But you can only use one HSMC card, so no extra GPIOs
By the time you are done, you could have bought a Spectrum Analyzer, but once you have this hardware, you could do say, SDR, or really anything you want.
Of course there are other ways around all this but it all will require learning a lot of things.
For example for Software Defined Radio, if you have a PC for $20 you can get this:
http://www.nooelec.com/store/computer-peripherals/tv28tv2-sdr-dvb-t-usb-stick-set.html#.U1BxEVVdVn8Need an up converter for 125MHz, throw in another $45
http://www.nooelec.com/store/ham-it-up-v1-0-rf-upconverter-for-software-defined-radio.html#.U1BxQ1VdVn8There is a lot of software out there for it too, that can do FFTs for example:
http://sdrsharp.com/http://www.winrad.org/I guess more details on what you want to achieve.