Most modern road and mountain bikes have very few, if any, hex head nuts and bolts.
A 15mm can be handy for centering some modern direct pull brakes, but it can be a cheap one or even an adjustable because that job doesn't need much force. A good quality 15mm is needed for most hub nuts on a fixed gear bike. A big pedal spanner isn't used often, but is a nice to have when it's needed. For little hex heads on things like mudguard draw bolts and racks, if you have those, ring spanners can be handy in confined spaces, or the ones with a little ratchet built in. Again, small bolts shouldn't need a lot of force so no need for the most expensive ones. A Y-wrench with 8/9/10mm sockets can be handy for things like mudguards. Get some decent cone spanners if you need them. If you buy cheap cone spanners you'll only probably end up buying the more expensive ones later.
Of course, if you find a good deal on a set, they're handy to have for lots of non-bike related tasks.
Ditch the cheap dumbell spanner immediately. When you put too much force on them the shaft can snap suddenly creating an extremely sharp and jagged fracture surface which then slices deeply into your wrist, resulting in a huge bloody mess and requiring a 999 call. Don't ask me how, etc.