To answer #1 - it really depends on the guitar, the circumstances, and the particular issues....I'll just give some examples of how I went about things....
My 85' Kramer Focus 3000 was a lemon - the locking nut broke, I replaced it. I got sick of looking for hex keys, I got a hacksaw and cut slots for a flathead screwdriver into the lock screws. Bridge pickup dies, I get a better pickup. High E keeps hanging on the pickup - I get a pickup ring and mount the pickup flush with it. Wiring goes bad, I build a new pickguard and add features I want to make it more Jaguar/Jazzmaster-like. Floyd Rose caves in and I'm totally broke - I buy a second hand Kahler and bolt it on with cylinder head bolts from a Lawn Mower engine. Headstock breaks, I add 2 screws to reinforce the weak area where the break happened. Wanted a floyd rose again - built a support using brackets from the back of a Computer and installed the original floyd again.
My Jag-Stang, in a total contrast, had all the parts there, but over time I Found things that would make it more convenient as my main guitar. Can't do phase changes with active pickups? So I rewired the bridge pickup switch into a pickup selector, and rewired the neck one to activate an EMG Pi2 Phase inverter on the neck pickup when slid towards the bridge. Wanted to get that Les-Paul-With-Neck-Pickup-Off switch flippy thing that chops the sound up - I left the forward of the neck switch blank and use that for that effect. I wanted to emulate single coil guitars - so I put a stupidly high value cap on the volume knob for a treble bypass - instant Tele on an active humbucker! Wanted more treble/high mids wide-open - I cut the trace inside the tone pot to make it no-load.
My Jaguar was bought with the intent of returning it to stock. So I got it in, I played it, I compared it with clips from the Fender Jazzmaster and Jaguar pages and found despite 500K pots and Cool Rails that it sounded perfect so I left those alone. But I did not like the feel of the Tune-O-Matic that the previous owner installed, nor did I like those rails pickups with all the black-space around them. So I saved my money, bought some Jaguar pickup covers and claws, cut them flush with the cool rails, installed them, found the screws too short, so I bought longer ones from the hardware store, and installed them. Then I yanked the TOM, ground out the wood filler with a Dremel, and put in a stock Jaguar bridge and thimbles. After that, I tackled the usual Jag bridge demons, but still wanted the same bridge/saddles/sound - so I got 2 stronger springs for pickups - put them on the high and low E saddles, angled those till the action screw holes act as a "lock", boxing in the other 4 saddles, and all was great.
To answer #2, it all depends on what I bought the guitar for. Some are BARGIAN instruments, like, for example, I'll buy a Crate strat copy and rebuild it and modify the wiring to sound better than original, and pot the pickups, and all that jazz, but I won't play it at all first, I'll just dig in and fix the faults that are already apparent before tackling any issues/preferences.
In the cases above, I played all those guitars for quite awhile beforehand. My Kramer lasted 2 years without mods before I started "mutilating" it. My Jag-Stang was stock for 6 months until I got the curiosity to pop the pickguard and find the atrocity the former owner did putting those EMGs in it. My Jaguar I played first to see if I really needed to spend $200-300 returning it to stock and "70's-ifying" it to get what I wanted (my benchmark was a 63' Jag with all original hot factory wound pickups), and found I only needed to spend roughly $20.
To me, it's all subjective, each guitar has it's own journey with me.