Firstly you will need to inform your insurance company as alloys (especially aftermarket ones) are usually regarded as a Modification. They may charge extra, they may not.
Many insurers have agreed you dont have to inform them when fitting winter tyres and wheels, but that exemption doesnt apply to your normal summer tyre wheels.
Check out your car on the following site
https://www.wheel-size.com/size/honda/jazz/2016/You are less likely to have problems with the insurers if you stick to one of the wheel and tyres size combinations approved by Honda for your model
EG 185/60R15 with 6Jx15 wheels ET50 or 185/55R16 with 6Jx16 wheels ET 53
6J means the width of the rim in inches . wider wheels such as 6.5J or 7J might still fit the car and tyres, but might upset the insurer.
the ET number is the amount by which the wheels 'stick out' from the hubs. too far out the tyres may rub on the wings , too far in the tyres may rub on the suspension. Ideally stick exactly to the Honda figure. You can sometimes get the correct ET on aftermarket wheels but often they are significantly different, yet claimed to be ok.
the wheels will also need to have PDC of 4x100 . That means 4 wheel bolts, spaced at 100mm Other sizes (4x108 or 5 bolts ) simply wont fit the hubs
The other figure is the centre bore , ie the hole in the centre of the wheel. On Honda this is 56.1 mm You cannot go smaller than this as the wheels wont fit the hubs. (eg original toyota Yaris wheels have a centre bore of 54.1 mm)
After market wheels often have a larger centre bore so they can fit multiple cars . But they should supply special adaptor rings (aka spigots) to bring the size down to 56.1mm. This should be ok.
when deciding on a tyre and wheel size check out the tyre price and available brands first . Some sizes are fairly rare ,only have a few makers, and can cost £30 + more per tyre
You might want locking wheel nuts if you havnt got them already. you should also check whether your current wheel bolts are suitable for the alloys.
If you decide to go wild and have significantly different wheel and tyre sizes you also need to check the rolling diameter of that tyre size, compared to what you have now , as this affects speedometer accuracy
Consider fitting all season tyres rather than Summer tyres. The better brands are really very good. Almost as good as the best summer tyre in summer -( and better than most budget summer tyres,) but with the advantage they are much better than summer tyres in winter. Alternatively if you plan on keeping the steels, and their tyres are due for replacement fit all seasons or even winter tyres to those rims . 15" tyres may be significantly cheaper and you can share tyre wear over two sets of wheels, and not put your alloys at risk of salt or kerbing.
