geofzx:
The first issue I run into is how I am going to power it (the tracker and the weather station). Not being familiar with weather station sensors and servo motors, will I need two separate power supply sources (e.g. 2 separate solar panels/batteries)? I don't want to have it plugged in, so that way I can place it wherever I want. I was thinking a solar panel might be good - I live in Houston, TX and it's pretty sunny here. That coupled with a rechargeable LiPo battery might do the trick? I have a nice 9V@1W solar panel from Parallax, and about 5 or 6 of those little garden light solar pannels that, if wired in series, might be able to get me up to 9V in peak day light (maybe 4 or 5V indoors) total.
LiPo batteries are a possibility, but they aren't as temperature tolerant (scroll down to "Temperature Effects" section), as some other battery chemistries. If the battery is going to be outdoors it should be an at least somewhat sheltered place, but still with at least some potential air flow (e.g. under a building's eave or deck). So it isn't exposed to the worst extremes of heat and cold. Of course if your system has the batteries inside a temperature controlled room, that would be even better.
On the other hand, while there are still limits on operational temperatures a sealed "gel" lead-acid battery would better tolerate exposure to both higher and lower temperatures, and would have significantly less risk of fire, etc... if it severely overheats. An appropriate SLA would be both heavier and bulkier than a LiPo battery pack, but reasonably sized (1 to 2 lbs and ~96 in3) 6 V and 12 V batteries are available in most hardware stores and some department or hobby stores. I'd recommend something like that for a "remote" weather station, even if "remote" really means a couple of yards from the nearest heated building in an unshaded case.
In any event, you'll probably need to regulate the power coming from the battery / solar panel so to a predetermined and known level before it gets to your electronics. The linear regulator most Arduinos would work with voltages that are ~7 VDC to 12 VDC, but it wouldn't work at all with a nominally 3.7 VDC LiPo pack and it wouldn't work well with a nominally 6 VDC SLA. Depending on the exact levels involved you might need to either step-up or step-down the voltage. To go from a range of lower voltages to a higher one (step-up) you'd need what's called a boost converter. To go from a range of higher voltages to a lower one (step-down) you'd need a buck converter, buck converters are also more efficient and generate less heat than linear regulators. There are boost-buck converters (a boost and a buck converter, and possibly some control circuitry, in the same module) that can do both, but they are generally more expensive and usually avoidable through proper planning and design.