Hi and welcome. A ten gallon tank would be too small unfortunately, even with a cage top attachment. Either for a Syrian or a Dwarf - they need a similar amount of floor space. The bin cage idea with your crittertrail attached sounds ok as long as the bin cage itself meets the required floor area - adding the two floor areas of the bin and crittertrail together doesn't work - it needs to be continuous floor area (in the Uk the minimum floor area is 70 to 80cm for the base of the main cage). If you don't have a crittertrail already I wouldn't bother buying one as an add on - you could use the money better towards a bigger main cage. Water bottles can be easily sorted in a bin cage - either by making or buying a bottle stand, or using industrial velcro.
As for ventilating bins - I believe putting holes in the top isn't enough - you would need a mesh panel somewhere. I know what you mean - I am not much of a diy-er! Once you start cutting bin cages and attaching mesh it means hot-knifing I think.
Are you in the Uk or the US - if you're in the Uk, there are good sized cages available that cost about the same as all the materials and tools needed for a bin cage. (I'm thinking the Alaska cage which is about £32 - good for a Syrian hamster but not a dwarf due to bar spacing). You can also get a Ferplast Duna tank for a dwarf hamster for about £34. (Is it Syrian or dwarf you are getting?).
In the US good sized cages are more expensive. There's a good one for a Syrian at $99. A lot of US owners use 30 or 40 gallon tanks. I'd say 30 gallon long tank minimum. I think in the US you can buy Zilla mesh lids so you don't have to make a lid so less diy.
If you want to have a go at a bin cage, Ikea's largest Samla bin is sometimes popular. Or if you have the space you could use an Ikea detolf as a tank (£40 Uk $60 US). This does need a lid making but it's easier than hot-knifing a bin cage! Just a few pieces of wood and some mesh cut to size in a hardware store (there are tutorials with the dimensions and instructions) and a stapler.
https://www.google.co.uk/search?q=ha...IVSV0UCh3-0QQF
DETOLF Glass-door cabinet - IKEA
Anyway before I start adding any more links I'll wait and see if you're in the Uk or the US (or somewhere else!). I'm guessing US when you mentioned 10 gallon tank.
There are some really good large bins in the US - Christmas tree bins I think.