streamline installation steps (FuelLabs#4380)

## Description
The current installation steps have rust and rustup dependencies at the
bottom of the page, and its not clear to the user that they need it in
order to install fuelup. This PR moves those instructions to the top of
the page to make it intuitive.

## Checklist

- [ ] I have linked to any relevant issues.
- [ ] I have commented my code, particularly in hard-to-understand
areas.
- [ ] I have updated the documentation where relevant (API docs, the
reference, and the Sway book).
- [ ] I have added tests that prove my fix is effective or that my
feature works.
- [ ] I have added (or requested a maintainer to add) the necessary
`Breaking*` or `New Feature` labels where relevant.
- [ ] I have done my best to ensure that my PR adheres to [the Fuel Labs
Code Review
Standards](https://github.com/FuelLabs/rfcs/blob/master/text/code-standards/external-contributors.md).
- [ ] I have requested a review from the relevant team or maintainers.

Co-authored-by: Camila Ramos <[email protected]>

docs/book/src/introduction/installation.md

@@ -6,7 +6,25 @@ The _Sway toolchain_ is sufficient to compile Sway smart contracts. Otherwise, n
 
 Installing via pre-compiled release binaries is the recommended way to get up and running with the Sway toolchain. Pre-compiled binaries for Linux and macOS are available. Native Windows is currently unsupported ([tracking issue for Windows support](https://github.com/FuelLabs/sway/issues/1526)). Windows Subsystem for Linux should work but is not officially supported.
 
-[`fuelup`](https://github.com/FuelLabs/fuelup) is the equivalent of Rust's `rustup` for the Fuel toolchain. It enables easily downloading binary releases of the Fuel toolchain.
+### Dependencies
+
+A prerequisite for installing and using Sway is the Rust toolchain. Platform-specific instructions for installing `rustup` can be found [here](https://www.rust-lang.org/tools/install). Then, install the Rust toolchain with:
+
+```sh
+# Install the latest stable Rust toolchain.
+rustup install stable
+```
+
+The Sway toolchain is built and tested against the `stable` Rust toolchain version (<https://github.com/rust-lang/rust/releases/latest>). There is no guarantee it will work with the `nightly` Rust toolchain, or with earlier `stable` versions, so ensure you are using `stable` with:
+
+```sh
+# Update installed Rust toolchain; can be used independently.
+rustup update
+# Set the stable Rust toolchain as default; can be used independently.
+rustup default stable
+```
+
+Now you're ready to install [`fuelup`](https://github.com/FuelLabs/fuelup), the equivalent of Rust's `rustup` for the Fuel toolchain. It enables easily downloading binary releases of the Fuel toolchain.
 
 1. Start by installing `fuelup` with the following command:
 
@@ -123,28 +141,6 @@ cargo install forc-lsp
 
 ## Installing from Source
 
-### Dependencies
-
-A prerequisite for installing and using Sway is the Rust toolchain. Platform-specific instructions for installing `rustup` can be found [here](https://www.rust-lang.org/tools/install). Then, install the Rust toolchain with:
-
-```sh
-# Install the latest stable Rust toolchain.
-rustup install stable
-```
-
-Installing `fuel-core` may require installing additional system dependencies. See [here](https://github.com/FuelLabs/fuel-core#building) for instructions.
-
-The Sway toolchain is built and tested against the `stable` Rust toolchain version (<https://github.com/rust-lang/rust/releases/latest>). There is no guarantee it will work with the `nightly` Rust toolchain, or with earlier `stable` versions, so ensure you are using `stable` with:
-
-```sh
-# Update installed Rust toolchain; can be used independently.
-rustup update
-# Set the stable Rust toolchain as default; can be used independently.
-rustup default stable
-```
-
-### Building from Source
-
 Rather than installing from `cargo`, the Sway toolchain can be built from a local source checkout by following instructions at <https://github.com/FuelLabs/sway>. The Fuel Core full node implementation can be built from source by following instructions at <https://github.com/FuelLabs/fuel-core>.
 
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