If you are both drivers the key thing to remember is that if you are under 25 and have had a full licence for less than three years you are likely to be penalised. If either of you are older than 25 or have 3 years experience, or both, then that is the person you should insure the vehicle for, with the other as a named driver.
The type of car is crucial, many imported cars especially from outside the EU, are expensive to repair because of the cost of parts, this also applies to specialist or niche manufacturers. The best insurance prices will be for standard vehicles say under 1.6, or diesels. Any type of performance vehicle will incur insurance loading, as will any modifications that you might carry out on the vehicle. Replace the standard wheels with a £2000 bling set of alloys, and the insurance will go up because of the cost of their replacement in comparison to cheaper standard wheels, in the event they are damaged.
If you live in a dodgy postcode( high incidence of car theft) then you will be loaded, as you will if you have any speeding fines or other convictions apart from parking.
Types of insurance are traditionally Third Party(TP), Third Party Fire and Theft(TPFT), and Comprehensive. Many people on a budget always assume that TP or TPFT are always the cheapest and until recently that was always the case. However it is not uncommon now to find that Comprehensive is the cheapest option, so try both on the comparison sites and see if there is a difference.
By far the most effective thing to do, which can sometimes reduce the premium by a couple of hundred pounds is to put a women on the policy who is over 50. This seems to reassure the insurers that the vehicle may be used by careful drivers at least some of the time, the older women perhaps mother in law? has to obviously have a clean licence. An older man may reduce the premium, but nowhere near as much as an older woman. The insurers seemingly consider all men of whatever age as budding boy racers.
Hope this helps.