BJT theory and practice - please help me understand
With a \$600\:\text{mA}\$ load (three devices to be simultaneously activated), a relay may be a good choice. There are plenty of relays available rated for vehicle use. Some of the really cheap small ones that are more often used with regulated \$12\:\text{V}\$ power supplies are rated to present a transistor load of about \$320\:\Omega\$. So this would mean a collector current (coil current) that is less than \$40\:\text{mA}\$. You'll have to decide on a specific relay, though, to know for certain because these things vary from one device to another.

You've indicated no more than \$20\:\text{mA}\$ as a switching current, but I think falsely concluded that you could rely on a \$\beta=100\$ for the transistor acting as a switch. There are two basic kinds of bipolar-based transistor switches commonly used for this application: a simple BJT or else a Darlington. The Darlington will drop about one volt when switched on, so your relay would lose that much. But most relays are rated to switch just fine with that loss. The Darlington choice would likely exhibit \$\beta\ge 1000\$ in some cases but generally not for switching due to some resistors that they usually include inside. So while this is a fine choice, I wouldn't consider more than \$\beta=200\$ for actual switching. A regular BJT (NPN) would likely exhibit \$\beta=10\$ or maybe \$\beta=20\$ for switching. But I wouldn't count on \$\beta=100\$ for a simple NPN -- especially one that can handle that much collector current.

Either way, if the relay coil current is no more than \$100\:\text{mA}\$ and given that your switching signal can comply with as much as \$20\:\text{mA}\$, I think both options (NPN or Darlington NPN) are still on the table. So that's good.

Your circuit looks fine. \$R_2\$ in either case doesn't need to pull down much current. So I'd just set \$R_2=10\:\text{k}\Omega\$. It's mostly there to make sure the transistor stays off unless intended to be on and to quickly remove any stored charge in the transistor. But it's value isn't critical and a lot of times you won't even see it present, at all. I think it's fine you keep it, though. The value of \$R_1\$ will depend on which transistor type. For the NPN, you'll want \$R_1\approx\frac{12\:\text{V}-1\:\text{V}}{10\:\text{mA}+\frac{1\:\text{V}}{10\:\text{k}\Omega}}\$ or something from about \$1\:\text{k}\Omega\$ to no higher than \$1.5\:\text{k}\Omega\$. For the Darlington, I'd probably use \$R_1\approx\frac{12\:\text{V}-2\:\text{V}}{\ge 500\:\mu\text{A}+\frac{2\:\text{V}}{10\:\text{k}\Omega}}\$ or something from about \$10\:\text{k}\Omega\$ to perhaps no higher than \$15\:\text{k}\Omega\$.

Either way, your switching signal appears capable of handling the situation. Just make sure that your transistor can handle the dissipation. This will be on the order of \$\frac{1}{4}\:\text{W}\$. A TO-220 packaged device would be totally safe. A smaller TO-92 device may get hot.