The Bitcoin you purchase on Swan is stored with a licensed and regulated Nevada trust company, Prime Trust, in cold-storage (offline) wallets. While you may leave Bitcoin in custody for as long as necessary, we recommend withdrawing to your own wallet. If you are not comfortable setting up a wallet, take your time to research your options first.
We recommend withdrawing Bitcoin when it reaches a certain threshold, in order to consolidate your coins for future spending. Bitcoin fees are not calculated by the amount of Bitcoin you spend, but rather by how "heavy" the transaction is based on the data it contains. By storing your Bitcoin in larger consolidated chunks, called UTXOs, you reduce the future fees you'll pay when you spend these coins.
Think of it like keeping $100 of cash in your wallet. You can store a single bill which is quick to take out, or you can store 100 singles, which can take more time to deal with. Bitcoin is highly divisible, so it doesn't matter if you store big chunks, as they'll get split as necessary for change in the future. But storing big chunks makes transacting with those chunks cheaper.
Because Swan withdrawals are free of charge, it is to your benefit to take advantage of that to consolidate lots of small withdrawals into one big one. For example, if you purchase $50 of Bitcoin every week, and set your withdrawal threshold to 0.01 BTC, you'll end up withdrawing roughly every two weeks at today's prices, consolidating two purchases into a single UTXO that you can spend later at a lower fee than you would have if you immediately withdrew. If you withdraw very small amounts, your future transaction costs may be high.
Setting thresholds also helps improve your privacy by de-linking your Bitcoin purchasing amounts from your on-chain transaction amounts.