Toyota or Honda would be my recommendation. Far more reliable than anything German if not quite as cool.
Age/mileage is less important than an owner who has had it serviced annually and got a stamp in the handbook from the service centre/garage that services it every year.
The Toyota Aygo,, Yaris, Corolla/Auris that kind of thing are good cars. Stick with petrol, which is simpler and cheaper to run in a small car anyway. There is no real saving in a diesel car unless you are doing probably double the average UK mileage per year.
Volvo also make some smaller cars if safety is a key consideration but they will be more expensive to buy.
If you can possibly afford it, a 5 door car is better and easier to live with and something the size of a Corolla/Honda Civic will be somewhat safer as it is easier to get good crash performance out of a car with more internal volume.
For discerning parents who are considering helping with the purchase of a first car, things like disc brakes on all corners, ABS an electronic stability program and air bags all around are worthy additions likely to keep your offspring safer on the roads. I'd also argue that air conditioning is pretty much essential these days and I also feel cruise control is a good way for young drivers to learn to keep their speed down.
Hybrid cars are in the main quite good now and the fact they are mostly automatic gearboxes is of no consequence as nearly all new cars will be automatics in the coming years.
All drivers -new and old- need to be paying attention to their tyres. Many brands have tread wear indicators on them these days but below a depth of about 3 millimetres wet weather braking and steering performance absolutely falls off a cliff and this is well before the legal limit of 1.6 mm. Have you checked yours recently?
Having various random brands of tyres on each corner is not a good sign in a used car nor are tyres which are all in various states of wear- the number of cars I see in public car parks with registration plates telling me they are less than 3 years old yet with bald or excessively worn tyres on them is scary. There are loads of second hand cars about, check the general condition, is there a dealers/mechanics servicing stamp in the handbook to match every annual MOT and does it have 4 reasonable tyres on it of the same make/model? Is the vehicle complete, 2 matching keys in good condition, is the owners manual and usual accessories with it? If not, walk away. Don't touch a car that appears to have been modified in any way either.
If buying from a dealership or similar business, always pay the deposit for the vehicle, however big or small, with a credit card. You get various consumer protections buying from a business and Mr VISA can be called upon if anything goes wrong. In general, reputable businesses will want to help customers provided they are being reasonable, if nothing else repeat customers are more likely to have their vehicles serviced and maintained by businesses they trust and this is where the real profit in the car industry is obtained anyway.Check the user manual. Engines need servicing before their annual mileage limit or at least annually as a minimum, whichever happens first. If you don't do this, don't be surprised if the thing catastrophically dies before 100,000 miles. Servicing and inspection goes beyond what an MOT test involves and it makes absolutely no sense to neglect a piece of machinery upon which your own life can actually depends.