Parallax addresses are Ethereum addresses. The wallet you already use can hold LAX once you add the network.
Choosing a wallet
Parallax uses Ethereum-format 0x addresses and the same keys. Import a recovery phrase and you get the same address, now on chain ID 2110.
Ledger and Trezor sign Parallax transactions with their stock Ethereum apps. No extra firmware or app is needed.
Every transaction commits to chain ID 2110 (EIP-155), so one signed for Parallax can't be replayed on Ethereum, and the reverse.
Network settings
Enter these under “Add a custom network” in your wallet.
Official desktop app
The official wallet for Linux, macOS and Windows. It runs a full Parallax node inside the app, so your balances and history come from your own copy of the chain, not someone else's server.
Third-party wallets
Independent wallets, not run by Parallax. Add the network with the settings above, then send and receive LAX as you would ETH.

MetaMask

Coinbase Wallet

Trust Wallet

Rabby Wallet

Atomic Wallet

CTRL Wallet

Brave Wallet

Phantom

Rainbow

Zerion

Frame
Using another wallet?
Any wallet that lets you add a custom EVM network works the same way.
A wallet connected to a public RPC tells that server your addresses and your IP address. For privacy, run your own client with its RPC enabled (--http) and point your wallet at http://localhost:8545.