I'd rather bring up a guitar for entertaining myself in theduring cool tropical nights beside the fire.

Why would I think about boredom in the first place?

The island itself mustwould be a very exciting place to be, and havingI would have a good time exploring it.

Next willould be a a good knife or a hatchet.

I think it willould be useful on an island.

And lastfinally... matches, maybe?

But they will end up soon't last for lon.g

Maybe something that could light fire and lasts for a very long time or maybe a bottle to fill it up with water.

Three Items I Would Bring if I Were Left Stranded Oon Aan Island

Title case is tricky, but generally, conjunctions and articles aren't capitalized:
- The Red and the Black
- Claudine at School
- The Myth of Sisyphus

This may help: https://www.dailywritingtips.com/rules-for-capitalization-in-titles/

The first thing I thought aboutidea I had was to bring a book.

But, obviously, even the most interesting book can becomes boring with time.

I'd rather bring up a guitar forto entertaining myself in the cool tropical nights beside the fire.

Why do I think about boredom in the first placefirst?

"In the first place" isn't wrong, but if you're implying that your priorities are wrong (rather than that you shouldn't be considering this at all), "first" is better.

The island itself must be a very exciting place to be, and havingI would have good time exploring it.

Next willould be a a good knife or a hatchet.

"Would" is slightly better here since this is a completely speculative essay.

I think it willould be useful on an island.

And last...ly… matches maybe?

But they will end up soonould be used up quickly.

"End up" indicates that the subject has gotten itself into something:
- I ended up having to wipe down the counter again because she made a mess carving the chicken.
- She ended up

Maybe I would get something that could light fire and lasts for a very long time or maybe a bottle to fill it up with water.

"Bottle" is already the object with "fill up," so "it" is not necessary.

Three Items Iif I Were Left Stranded Oon Aan Island

Some words (prepositions) shouldn't be capitalized in titles:
https://www.grammarcheck.net/capitalization-in-titles-101/

But, obviously, even the most interesting book becomes boring after a while.

Added "after a while" to make it sound better

I'd rather bring up a guitar forto entertaining myself in the cool, tropical nights beside the fire.

When you have two or more adjectives together, you need commas to separate them. So, it should be "cool, tropical nights" instead of "cool tropical nights"

Why would I think about boredom in the first place?

The island itself mustwould probably be a very exciting place to be, and having, and I would have a good time exploring it.

Changed the sentence to sound smoother. Since you are thinking about hypothetical situations, you use "would".
https://www.ecenglish.com/learnenglish/lessons/wishes-and-hypothetical-situations

Next will be a, I would bring a good knife or a hatchet.

I think it willould be useful on an island.

And last...ly, perhaps matches maybe?

I think "perhaps" sounds better here, but you can also use "maybe". If you used "maybe", you would put it before "matches".

But, they will end up soon.ould probably be all used up after a short while.

Sounds better this way. If you have something, and you use it until there's nothing left of what you had, you say "used up", not "end up"

MaybeInstead, perhaps I would bring something that could light fire and lasts for a very long time, or maybe a bottle to fill it up with water.

"Instead" works nice here, because you said the matches wouldn't be good, since they would be used up quickly. So here, you give an alternative, therefore you use "instead"