Hi there and welcome! Sorry you didn't get replies before now
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A 70cm tank sounds fine - how deep is it? It would be much better than the Home Sweet Home cage and you could use some of the contents in the tank as toys maybe. Just check the tube is big enough - sometimes Syrians grow quite large and can get stuck in tubes. I wouldn't use the little house though. It's best to have a house open onto the substrate so they can burrow down and something a bit bigger that is nice and dark inside - an upturned shoe box with a hole cut in for a door makes a good house/nesting box. A tank will mean you can give a good depth of substrate for digging and burrowing which is good! Other than that you'll need a Syrian sized wheel. Unfortunately cages come with teeny tiny wheels that are sometimes even too small for dwarf hamsters. They need to run with a straight back so usually an 11" wheel is about right. The height of your tank might dictate the wheel you get - some are taller than others for the same size diameter.
Some tanks are only about 30cm deep which would make it a bit small if it's only 70cm long, that's the only thing. It could do to be at least 40cm deep really.
Anyway you said you had plenty of toys already so that's good. I like this video on youtube where someone shows how to make a mesh lid for tank
https://www.youtube.com/watch?v=Mdz3bLmegZQ
I know you said you were planning to save for something bigger, but have you seen the detolf hacks? You get a good sized tank for a cheap price with those, and again just made a couple of lids for it.
The detolf only costs £40 although needs something to stand on really which can bump the price up a bit - it sits well on two 4 x 4 kallax units which can also provide storage under it, or a cheaper option is two of the £5 Ikea Lack tables. Just a thought as it can cost a lot less than other options if you're saving up and have the space!
It's basically a glass cabinet from Ikea that you tip on its side and leave the door off.
https://www.google.co.uk/search?q=ha...t7Bz8Q_AUIBigB
I don't know how secure that lid on the video is, but as it overlaps the outside of the tank you could maybe use a bit of industrial velcro between the side bit of the lid and the tank. Or put a book on the ends! Someone else might have more ideas on that front.