I'm avoiding chores - so this will be a long ramble....
TLDR1 - go for option 2
TLDR2 - a sound guy is going to do the easiest thing to guarantee a half-decent consistent sound
TLDR3 - make sure you can get the FOH sound you want out of both DI box's 1/4", XLR and your amp's XLR out (if it has one).
A lot of this depends on what sort of gigs you will be doing. If you're going to be the only act and/or you're hiring the PA / sound guy directly - then what you say goes. But as you say you're a bit of a novice playing live, I would guess the venue will have it's own FOH or regular PA team they hire in.
Of course, if it's a small pub gig, then the PA will probably only be for vocals so it's then down to what's coming out of the amp.
Let me paint a picture....
Let's say it's a university venue on the college/indie circuit. 500 capacity. It's the regular indie night where they get an up and coming national band to headline and two or three local support acts. It's not a silent stage and for room, it's expected that a lot of the backline is shared. Often, the headliners will refuse to share their gear so the main support will have to.
The main act roll in with attitude and a lot of vintage valve gear. The bass player has a fridge of an old Traynor - with no pedals. the sound guy will run an XLR cable to the back of the stage, use a passive DI box (on phantom power), with its 1/4 output plugged straight into the amp. Then gets the bass player to plug into the Di box.
Sound check done - it's your turn. 99 times out of a 100, he is not going to unplug the XLR, move the cable across stage, wait for you to set up your pedals and check they're working before plugging in to your DI box - and then go back to the desk to turn off phantom power. Also knowing that the next band to sound check will not be using your pedals and so will need the house DI box set up again. There are too many possible problems/delays there. You may be lucky, he may want to set up separate channels on the desk for each band's instruments - and so have a different XLR cable for each, but I doubt that will happen in most cases.
So either, at change overs, it's expected all bass players uses the same DI box - or if you're lucky, as the other support acts are sharing your amp, he'll unplug the XLR from their DI box and plug it into your amp's XLR out if it has one.
So I would say, regarding your signal chain, the most important thing would be to get a consistent sound out of both the XLR and 1/4" of your RNDI. If you're using a house DI to FOH, consider using your DCX and keep the stage amp reasonably flat for monitoring. If the XLR is from your amp, do the same but make sure the XLR out is pre-EQ (or have it post with possibly no DCX).
End of ramble....