you'll want a couple hub bearing cone wrenches (EXTRA thin)... Park tool 13mm and 15 mm sizes... A QUALITY pair of side cutters to cut Cables and cable casings. i bought a pair of "special" cutters for the cables/casings, and TOSSED them into a drawer after the first use... You'll want a GOOD floor pump with a built in gauge to air up tires... Buy the correct type of wrenches for the Bottom Bracket cups, and get a Park tool Crank remover...... get the correct Freewheel or FreeHUB remover tool too, and IF you have a Cassette type freehub, then you'll need a chain whip too... get a good one because the "cheap" ones tend to break at the most inopportune times....

SPOKE WRENCHES... get a set of good ones, then plan on replacing the one you use the most often, or just go to a decent shop with a wheel, and they can fit up the CORRECT size for your spokes... there is VERY LITTLE difference between the 3.2, and 3.3mm sizes, and i've replaced many a rounded off nipple because the 3.3mm will KINDA work, right up to the point where it RUINS the smaller 3.2mm nipples... Park Red(3.3), and Park Green(3.2) ones are the most used in my tiny shop, btw...

Chain breaker... you'll want one... get the Park tool CT-5, or it's big brother... it works fine, and will outlast your bike by many years... IF you need one, they sell replacement pins for them, even! The cheapo ones from across the Pacific might just break the FIRST TIME you try to use it! Been there, had that happen many years ago... that's what i get for trying to save ten bucks, i guess.... sigh....

a decent set of metric allen wrenches will be a must, too... i use the ones with the ball end on the long side... handy for spinning screws in tight spots, like under the seat... that's a 6mm on almost all seat posts.... the 8mm will remove/tighten the crank bolts... and the 3 or 2.5 will come into use for twist shifter set screws... you probably already have a set of metric allens, though, eh?

Tire irons/spoons/levers... i use a REALLY dull #2 flat screw driver that i custom bent, and a decent METAL tire lever... DON'T bother with those cheesy plastic/nylon ones... they are just about worthless.

your other metric wrenches, and basic tools, will work for most all other needs...

Start with the wheels/ hubs, then work your way up... and typical Automotive grease is too thick, it won't flow back onto the bearing surfaces... get a tube of phil's or park grease... both are water-resistant, and formulated for bicycle use.