The wallet you deposit from should be one you control. Custodial wallets and exchange accounts defeat the point.
Bitcoin
Sparrow is the privacy-aware desktop choice, with coin control and hardware wallet support. Electrum is the lighter option. Both hold your own keys.
Monero
Feather is the light desktop wallet that needs no full node. Cake is the mobile-friendly one and carries a Bitcoin-to-Monero swap. Both keep your keys yours.
What to avoid
Custodial exchange wallets, browser-extension wallets, and anything that will not export a seed phrase or that syncs to a cloud account by default. If you cannot hold the keys, it is not where your coin should sit before a deposit.