[hvalentim]

My latitude is 31 deg N, and I get a fair amount of sun. I guess I'll have to see what the winter's like.

Your location does seem to be sunny. Using hourly averaged data over 10 years from the nearby Savannah Airport and assuming an unobstructed horizon, for a 24/24h 1W draw, PvSyst recommends a 9Ah battery coupled with a 7W solar panel (targeting 4 days of autonomy with a 5% chance of loss of load).

But don’t take my word for it, grab the tools below and do your own reasoning, trying different scenarios.

PvSyst
http://www.pvsyst.com/en/software/download
Fully function evaluation mode, limited to 1 month.
Closest location included in default weather data is Atlanta. You may wish to grab Meteonorm to get data for a location closer to you.

Meteonorm
http://meteonorm.com/en/downloads
Works in a demo mode for an unlimited period. Saving is restricted to five sites.

Instructions on how to import data from Meteonorm to PvSyst:
http://files.pvsyst.com/help/meteo_import_meteonorm.htm

Also, bear in mind it may be wise to plan ahead for future stuff you may one day add. For instance, the values above do not consider having a fan running (easily another 100mA).

The less you discharge the battery the more it will last. Longevity wise, you ought to design things as to ideally not taking more than 25% out of it and never more than 50%.

As a matter of contrast, for Glasgow, Scotland, under similar circumstances (1W 24/24h draw, clear horizon and 9Ah battery), the simulation recommends a 37W solar panel.

Concerning the DC/DC converter I am using a TracoPower TSR 1-2490 myself, and thus far found no problem. It fits nicely, protruding just a couple of mm on the external side of the RX board. Of course, in the end, it does have the exact same utility of a LM7809, except it costs more, it has a potential risk of generating radio noise (cannot comment on that since I do not have a WD unit nor do I use the retransmit feature of the base RX unit) while being a bit more efficient and taking in an higher voltage if needed (up to 36VDC against the 35VDC supported by the Fairchild LM7809ACT).

Edit: Corrected the maximum input voltage of the LM7809ACT.