Most mixers have direct outs. If your's doesn't, it probably has multitrack buses - connect their outputs to the inputs of your recorder and assign each "tracking" channel to the bus which has it's output connected to the input of the track you want to record.
If the console is split design, it probably has dedicated tape return inputs too. It might be better to connect the recorder outputs to those inputs, so they'll appear on the right hand side of the console on the monitor channels. Many split desks have switches on the channels to switch the tape return from monitor channel to main channel, but not all do, so it might still be better to connect the outputs from the recorder to the line ins. You have to find out what works best for your workflow and what gives you the most flexibility on the desk.
Of course there is a lot of great outboard, but great compressors are quite expensive. If you want just "a better experience", maybe think of some reverbs, because you'll want to use them post fader and this can become difficoult in a hybrid setup.