I don't use Logic but I do use Studio One and each channel has a set of presets broken down by instrument and only uses stock plugins. If Logic has this function it may help as a starting point.
Do yourself a huge favour though. When starting out recording, forget about buying plugins from 3rd parties, avoid that rabbit hole and Instead learn the ones in the DAW. This will save you a lot of money, remove you from the plug in rabbit hole, and more so, allow you to learn which plugging work for you and which dont, then replace the ones that dont.
As mentioned above, the Axe sound should be close to perfect. If you are compressing and eqing heavily in the DAW, I would rethink your patches in the Axe. Not only will this make sure that the signal you record is good, it will also offload a heap of CPU processing (remember shit in, shit out). A great way to do this is to either use the Looper in the Axe to record a loop of your playing then start to create the sound in your head, so you are not also hearing the dry guitar, or learn how to reamp: the latter being the better option so you can hear the changes in context of the song.
A good general rule of thumb, expecially if you are doing anything effects laden is record everything that is non modulation into the DAW (amp, cab, overdrive, compression, eq etc) and use the modulation plugins (delay, tremolo, flanger etc) in the DAW for more control.
Just a few things to consider.