I concur on the Park Tool Video Series. Covers the basics very thoroughly.
In addition to typical sockets and Allen wrenches, and a bicycle multi tool for travel, you can get started on occasional maintenance with a cheap combo bicycle tool kit off Amazon as well, and later upgrade the ones you find you use a lot. A couple of things you may want that you just can't use household tools for:
1. Pedal wrench - most combination and adjustable wrenches are too wide and will scratch things
2. Chain tools (Master link pliers/Chain splitter/Measuring tool) - if you have or want to add a master link to your chain for easier maintenance, the right pliers makes the job SO much easier.
3. Cassette or freewheel socket (depends on which one your bike has) - used to replace the cassette when it wears out in a few thousand miles.
4. Chain whip - used to hold the cassette while using the removal socket.
5. Chain measuring tool - the quick gauges are fine for snapshot checks. Vernier Calipers are the most accurate if you already have them.
6. Valve core removal tool - some stainless valve stem caps have one built in to the top - but a proper tool is nicer.
7. Spoke wrench - get one of the multi-size tools.
8. Hub and bottom bracket wrenches/sockets are getting into intermediate surgery, but also should be bike-specific to avoid damage
Optional add-on: A light duty torque wrench in the 3-12 n/m range if you like to be accurate and not strip light bolts.
Park Tools are always good/great quality but very expensive for the non-enthusiast - although they make some cool combo tools that do several of the jobs listed above in one tool - like the chain whip pedal wrench. I use 'Pro Bike Tool' or 'Oumers' as a cheap casual-use alternative. Use caution with un-reviewed no-name stuff as it can be more frustrating or damaging than it's worth.