You have not said what you want your Uno to do, how many hours per day it needs to do it or whether it will have any external peripherals that also use energy.
You can usually organize a program so that the Arduino goes to sleep to reduce its energy requirement - although that is a lot more effective if you just use the Atmega 328 chip without the rest of the Arduino baggage.
Before you can specify a solar panel you need to know how many watt-hours per day your Arduino will use.
You need to allow for a lot of energy inefficiency in the battery - I suggest at least 50%.
Then, taking account of local sunshine patterns, you need to figure out what size of solar panel is needed to deliver the required energy. Keep in mind that a 1 watt panel will only produce 1 watt in bright sunshine when the panel is directly facing the sun.
If you want your Arduino to run continuously you need to size the battery so it has enough capacity to keep things going during a succession of dull rainy days.
Personally, unless weight is a problem I would use a 12v lead-acid battery because they are very safe and a very simple solar regulator would be sufficient.
If the battery capacity is very much larger than the solar panel it may not even be necessary to have a regulator. I charge a 200Ah battery with an 80Ah solar panel without a regulator. The max output of my panel is about 5 amps which is not enough to overcharge the battery. And most of the day-time the output of the panel is only 1 or 2 amps. (In case of doubt I am not suggesting you need a 200Ah battery for your Arduino).