MiXiN - the frequencies involved in a medium wave transmitter are low enough that you don't have to take special precautions like you have to at VHF. You can even build transmitters on "Veroboard".
I'll put a basic medium wave design up here shortly. I'll also include all the design equations, and explain how to use them. These are important, because they'll allow you to scale the design for the range of frequencies that you're most interested in (probably at the higher frequency end of the band), and also scale for the power output that you want. For lower power, I'll include a "worked example" and a Veroboard layout.
The mathematics isn't difficult! You're calculating the number of turns of wire for a particular value of inductance, and you're calculating the output impedance of the PA and thus the turns ratio of the autotransformer that you'll use to transform that to 50Ω (or any other preferred match impedance). You're just substituting numbers into an equation and cranking out the answer - that basic algebra at school really was useful!
The modern power FETs that we use for the output stages on medium wave are usually rated for a few hundred Volts and several Amps, yet they still cost pennies! (I just built a 400W VHF PA, and the dual FET that I used - a Philips NXP one - cost almost £150!).
The logic ICs that we will use are just pennies each (unless you go to Maplin

) and the crystal is less than a pound too. The only (slightly) difficult bits to get will be the ferrite parts, but I'll suggest sources for those (though the manufacturer does small orders themselves). We'll need a few small toroids, and you're going to have to learn how to wind coils neatly on to them.
The modulator uses an audio power amplifier IC, which is (essentially) just a big op-amp. I'll also give the option of a few bells and whistles if you want to add them. These include a basic modulation compressor, a modulation depth indicator, frequency response shaping and the option for remote switching through your link.
I'm just finalising the notes, taking a couple of photos of a work in progress, and drawing up a neat 'n' tidy Veroboard layout. It won't be expensive to build and it won't be difficult, either.
You're going to need a multimeter, access to a frequency counter (for a one-time calibration), and access to a 'scope to set up the modulation depth indicator and to check the output waveshape and what the modulation looks like. I'll even mention "trapezoid tests" if anyone wants to get that precise!
You have to remember that a "5 Watt rig" might deliver 5 Watts into the load when unmodulated. On 100% modulation peaks, it will be delivering 20 Watts! Manufacturers call this the

"Peak Envelope Power" and this is generally four times the unmodulated power. It's a more impressive figure than the blank carrier power! This means that we have to provide a well overrated PSU and plenty of smoothing capacitors, and we have to expect to get rid of plenty of heat because a basic AM transmitter is quite inefficient - it makes as much heat as it does make RF!
The power levels we're considering (at first) may seem very low compared to the hundreds of Watts on FM. However, medium wave isn't confined to the horizon, and with a good aerial and earth system and a clear frequency, you can cover a huge area just using modest power. Night time coverage can be reduced by the arrival of the skip signals from Europe, but if you've found a reasonably clear frequency (and there's quite a lot of them now that the French have gone), you'll get into Europe!