If you're referring to Swagelok B-OVM2-BKB Needle Valve, its both threads are 1/8'' in size.
When looking for a output tube connector type ordeal. Make sure you look for 1/8'' Nut. The 1/8'' Nut is needed in order to screw onto the above Needle Valve used.
Referencing the 3rd item on the picture as a example. Watts A-15LF is a 1/4'' x 1/8''.
This is used on Needle Valve that is 1/8'' x 1/4''. 1/4'' being as the Male output thread which the A-15LF has a 1/4'' Female Thread to thread onto the 1/4'' output thread of the Female side.
The Swagelok won't be able to use this part number because the Swagelok is 1/8'' to 1/8''. If you do want this Nipple type Tube connector, look for in a 1/8'' x 1/8'' size. I'm sure Homedepot has it.
You can also also use this Barb connector also. You will have to look for it yourself at Homedepot. I have not gotten a part number down, but 3-4 people are using it with this setup as well. Again, since the Swagelok is 1/8'' x 1/8'', you will need to find a 1/8'' Barb to tubing connector. This is a photo of what it looks like.
As far as co2 tubing size, I couldn't tell you. It just all depends on what you decide to get. I don't recall standard aquarium air tubing size. Most people don't, we just buy it and plug it in to our air pumps. Either way, using standard air tubing size for a co2 gas setup is not the way to go. The standard air tubing size can burst. Use co2 gas tubing is highly recommended.
Keep in mind, Homedepot's smaller size Co2 tubing that they carry is SVEB10 or SVEB20. 10 is for 10 feet, 20 is for 20 feet.
If you're going to buy the Compression Ring setup, this is all based on what Output coupler you buy. Compression Ring itself, cylinder ring inside the nut, comes in 1/4'', 3/4'' and also 1/4''. The Compression Ring it used in conjunction with a Output coupler.
When you get your Swagelok Needle Valve, take it to Homedepot and head over to the plumbing department and start ripping connectors that will have a female end which needs to be 1/8'' to thread onto the Swagelok Output thread. That's the best bet, I'm sure you'll be able to figure it out from there as far as a Output tubing connector piece.