When switch company, should I transfer 401k to new company's account, or my personal Rollover IRA at Vanguard or Fidelity?

I feel my personal account is better for freedom. Is it right? Currently I have company 401k (which I transferred from previous one), and at Vanguard I have \- Brokerage account \- Traditional IRA Brokerage (0%, I only use this for Roth backdoor conversion) \- Roth IRA Brokerage I do backdoor Roth conversion of 8k annually. My largest fund is in 401k, followed by Brokerage account then Roth IRA. Roth IRA income limits $153,000 and my income is above that. New company offer 401k match, and I will take advantage it. Just in addition, is it still possible to roll over my previous company's 401k to personal IRA? I am under impression, if I do roll it over to personal IRA, I could not roll it back to 401k (of any employer down the road).