In the typical 985x module, there are two sinewave outputs: one goes through a lowpass elliptic filter, with a terminal load of 200 ohms. The other is unfiltered, with a load of 100 ohms. About the filter, take a look at the
documentation of the module, keep in mind there is an errata, L1 is obviously 470nH, not uH. I get a 3dB frequency of 75MHz; it should keep away major aliases up to 49MHz, so you should use this output to avoid harmonics in your transmission.
Since the AD9850 uses a current source at the output, the waveform is a 1V amplitude sinewave going from ground to a peak of 2V. The output of the module is low impedance (100-200 Ohm), so you should probably use a buffer (a single FET common drain would work, or a AC coupled emitter follower-- remeber the output goes to ground) to avoid distorting the output of the DSS module. Then you can amplfify the voltage if you need it (remember it's already a 1V amplitude singal) and/or amplify power. How much power do you need anyway? The low power bands don't allow much more than a few mW, if I remember correctly.
About the antenna, take a look at
this calculator. The wire diameter matters. Anyway, you'll find a very low radiation resistance , and a big capacitive reactance. I think the usual cure is a series variable inductor that is manually tuned at the required frequency for maximum performance.