Out of the gate, I feel as though 5th edition more than any previous D&D system provides for a vast array of character concepts and combinations – feats and backgrounds, along with the incorporation of the eldritch knight, arcane trickster, elemental monk, bard, paladin, ranger, and pact-blade warlock into the core ruleset in my opinion elegantly blurs the lines between spellcaster, warrior, and rogue. These classes seem to be adequately balanced to work in a party alongside champion fighters, thieves, barbarians, and battlemasters. And the list of options within the classes is only going to get larger. Multiclassing, in general, is not needed – the combinations wrapped in a single class are right there in the core PHB, and can be further tinkered with through backgrounds and feats such that members of the exact same subclass can be completely different.
Therefore, you should consider multiclassing off-limits, unless you have a spectacularly compelling character concept. One, two, or three-level dips in a class to cherry pick synergistic abilities are flat out. I dealt with a ton of that in 3rd edition and I have no intention of repeating it. I have nothing against that playstyle and there are tons of campaigns out there where the power-combo itch can be scratched, but it kills the fun for this particular DM to try and maneuver around the madness and still attempt to keep things balanced for the rest of the party.