I don't know one brand that is better than another. I think I used Minwax or something you can pick up at the H-D. Most polyurethane sealers are pretty comparable. It should be exterior grade to withstand the UV light and moisture.
I would recommend at least 3 coats, but more is definitely better if the surfaces will be exposed to water - more coats for water-based products over oil-based, too. Depending on the humidity, you may be able to apply coats within only a few hours of one another if you are using water-based sealer; oil may take a day or two.
Let me share what I learned the HARD WAY from my recent project:
Water-based is nice, but it blanches (turns white) at drips and if water is allowed to sit on the surface. I used water-based on my latest project... I will use oil-based from now on. Oil-based requires cleanup with solvents but I think it provides a nicer finish. If it is tinted, make sure to stir regularly or the product with separate and give you an uneven color. I wiped on the stain but bush applied the clear coats.
Wear latex gloves but know that the gloves will leak, and you will have espresso-colored fingers for days.
Be sure to back brush away from edges to avoid uneven application and brush marks (voice of harsh experience

) and be on the lookout for drips along corners and edges. Let it cure for a least a week, longer is better - an okay but not definitive test is the "smell" test. If you can still smell the sealer, it needs to keep curing.
Honestly, I thought staining and sealing the wood was the hardest part of building the entire enclosure. Have fun!