Preparing for the rain and for the sun, I have a lot of experience and I strongly recommend 2 companies for their hats and rain/sun slickers.

Choosing between an oilskin hat, a Tilley hat, and a cheap knockoff of the Tilley.

• I have purchased several cheap knockoffs of Tilley hats - and nothing comes even close to a Tilley hat. The Tilley hats are more durable, they stiffen up real nice in the rain to keep the rain off and they scrunch real nice to fit in your carry on. Go with one of the traditional style Tilley's. Don't go with one of the beanies, or the mesh, or the winter hats or the fedora or the broad brim. I know you might be tempted to go with the broad brim, I own one and I use it for gardening, but it is too floppy in the rain and it flops down in front of your eyes. Go with the traditional styles like one of the T1 or one of the T5.
• The right oilskin hat is the ideal Costa Rica rain hat. I'd recommend Kodiak, Riverguide or Grizzly - there may be others that are good too. In my opinion: don't go for any of the mesh ones or the baseball cap or the North American cowboy (think "Western" movies) The downside to these hats is you really should not crush them or sit on them. Yes I have, and they do recover, but they never are really quite as easy to shape after you sit on one or run your car over it. The nice thing though, mine has been run over by a skid steer (think "bobcat"), been stepped on, been crushed by sitting on it many times. It looks beat up - not a great 'Sunday go to church' hat anymore, but it still works perfectly - I had to krazy glue a bit of ripped material once, but that it is.
• Both Tilley and the Oilskin hats I'm recommending come with a chin strap or chin and back of head strap. This is important because you do not want a tight fitting hat. When the wind blows, you don't want these hats held on by friction, you want them held on by the strap. That way, when you are using it in the hot sun, it fits loosely and lets air flow around, minimizing sweat.
• On disadvantage of the Oilskin hat is it is dark colored and as a result you will sweat more in the hot sun. Personally, I wear my oilskin hat on the plane and I pack my Tilley T1 or T5 in my carry on. Then I wear the Oilskin in rain and the Tilley in sun. When the Tilley gets all sweaty, I turn it inside out and let the sweat band dry while I'm getting the other side sweaty. It looks unstylish - but it works!
• If I could only have one of these hats, I would take the oilskin if I was travelling in the green/rainy season and the Tilley T1 or T5 if I was travelling in the dry season or shoulder seasons.

As far as slickers go. I have an Outback Stockman oilskin duster. The stockman is longer, providing more rain protection for your legs. It and the shorter Low Rider duster are designed to work perfectly when riding a horse or out walking in your field, so they are in my mind perfect for walking in Costa Rica sun or rain. They are fairly light and won't provide a lot of extra warmth in cold weather: in Canada where it gets down to -40C in my area, I wear a sweater or a 2nd shirt and sweater depending on how cold it is, but in Costa Rica, I just wear a light shirt under it. In the heat and sun, it can be too much though - so I wear it for short trips in the sun as very convenient sunscreen or when it is raining, but not for long walks in the sun - it is too hot.

Where to buy:

• OutbackTrading.com (no I do NOT make ANY money from you clicking on this link - I just love their stuff and have been wearing them since about 2014) is a great place to get a perfect oilskin slicker or oilskin hat
• Tilley.com (no I do NOT make ANY money from you clicking on this link either - I just love their stuff and have been wearing them since the early 1980's when they were a brand new company.)

As far as camera's and cell phones, I've done everything from a plastic bag to a waterproof hard case for a camera I owned many years ago that I made myself out of plexiglass and silicon sealant for the waterproof part. It was good down to 3' below water - I didn't try it lower than that. So I don't have any real suggestions on this even though I've used a lot of water proofing/water protecting equipment through the years. The costs vary greatly and what they do and how inconvenient they are varies.

Currently for cameras, I use a plastic bag for my Nikon and Canon equipment, a plastic sheet for my 4x5 view camera, and a waterproof bag I got online for $3 for my cell phone. All work for me!

I also don't have any suggestions for boots. I wear Red Head heavily insulated high boots for -65C to +50C (I like the insulation at both extremes!) but I have duck feet - 9EEEE in the front, 9 in the back) so I have very limited options for good footwear, most footwear that claims to be 'wide' is not wide enough for me. I also wear crocs, but they wear out quickly walking on gravel, so I use them on sand, grass and airplane if I don't have my hikers with me. I wear the hikers on the plane then because they would take up way too much room in my carry on or luggage-and I like to take a lot of stuff ranging from computers to cameras with me when I travel, so wearing all the bulky stuff on the plane lets me take more of my "stuff."