I generally prefer familiar to NOT be an easy out for things like scouting, finding traps, providing advantage, and others. I also dislike their disposable nature. "Oh, that's okay, I'll just summon another one.", which is a common refrain around my table.
I'm working with the SRD(?) familiars as a base, which provides for tougher familiars, a variety of small buffs for the caster, and improved abilities over time.
The trouble I'm having is figuring out exactly what a familiar is supposed to be? I did some googling around to see what, if anything, was out there from lore perspective (either game related or historically) and really couldn't find anything. Pet? Connection to Other? Guide? Assistant? All of the above?
The second sticking point was what to do with it. As mentioned by TheSword, I didn't want it to be a second character, and mostly just take up space in the initiative order, but where does it go? In a wizard's pocket? Its just there but can't be harmed? Etc. TheSword's idea about the familiar providing some benefit without actually being a physical thing is something I'll consider.
I can remember in the old old days, when one of us had a familiar, it was "in the pocket" until it wasn't. And was mostly immune to damage there. Unless, of course, you were hit by a fireball or lightning bolt, or disintegrate and needed to start making saves for everything on you. Ouch.
I also tweaked the Find Familiar spell (thanks DND_Reborn for the example) to be more costly, and to have a severe cost to the wizard for having the familiar die. But balancing that against the benefits is the challenge. I was also trying to add in a research benefit to the familiar, so that it is something more often found in a wizard's lab, rather than out adventuring.