OK, given the clarifications in comments (that there's no hot water tank, so this is presumably a combi boiler doing "instant" water heating, and that the bathroom has a radiator and no towel rail):
Hot water
There is no hot water storage - the boiler warms it at the time that you run the tap - so timings are irrelevant to this. The only variable left is the temperature that you would like hot water to be provided at, which is probably the dial marked for water on the boiler is. This is partly down to personal taste, but as a starting point I usually tune it so that the thing that I use the hottest water for - in my case, washing up - can be done with water straight from the hot tap. But, it probably makes little difference in energy terms. Be careful about setting it too high, or you may be able to scald yourselves on tapwater.
One question that I forgot to ask in comments was whether the shower actually uses hot water from the boiler, or whether it does its own electric water heating - many do - but this doesn't make much practical difference, because there's little you can do about it either way.
Heating
You have a few more controls to play with here.
Set the timer for when you would like the heating to be on; this will presumably require negotiation.
If you both go out during the day then I suggest a period in the evening (for comfort, and for having a warm bedroom when you go to bed) and a period just before you get up in the morning (so you're not shivering when leaving your duvet!). There's no point in heating a house when nobody is there, and unless you've in a very cold climate (or there are health reasons), no point in heating a house when everybody is asleep. When choosing the times, bear in mind that the house will take some time to warm up from the start time that you set - perhaps anywhere between 10 and 60 minutes, depending on many factors. Some experimentation will be needed.
Note that contrary to myth, it is not more energy-efficient to keep a house warm throughout the day than to let it cool off when unoccupied.
The dial for heating on the boiler will control the temperature that water is heated to when sent to the radiators. Think of this as the rate at which the boiler can transfer heat into your rooms. The higher this is, the more "power" the system will have, the faster it will respond, and the better it will cope with cold days, but the less energy efficient it will be (because heat leaks faster from hotter pipes).
You may find that having this set high causes a "cycling" behaviour where the boiler runs for many short periods with gaps inbetween, and that having it set lower means that it is on more constantly, at a lower power. This may be important when you're considering the noise in your bedroom, and so long as you don't put it so low that the system can't heat the house, you can probably tweak this without your housemate even noticing! See also this question: Setting radiator temperature to save energy
The third control that you have here is the overall house thermostat. If this instrument thinks that the house is warm enough, then the heating will be switched off - regardless of what the individual thermostats on the radiators reckon. If it's been sited well this shouldn't be a problem. You should use this to set the overall temperature that you would like your house to be at.
The fourth control that you have here is the individual thermostats on the radiators. You can use these to control the relative temperatures between different rooms, allowing some variation from the setting of the main thermostat. You'll only get these right through experimentation and (in shared areas) negotiation, but as a starting point I would have the bedrooms slightly cooler than the living areas. Sometimes these devices are labelled with temperatures (Fahrenheit or Celsius) and sometimes just with numbers. If you have temperatures, ignore them - these things aren't usually very well calibrated - and just go with trial and error :-)
Now, in summer, you could just rely on the thermostats to keep the heating off... but if the temperature dropped slightly below the hall thermostat's setting, it would fire up the boiler and burn a load of fuel to raise it back again, when you or I would know that the sun would do that in half an hour anyway. So you may choose to turn the heating off completely. If you want to do this, do it by turning the heating dial to minimum, and then it will probably never come on. Do not use the boiler's overall "off" switch, as that will probably turn off water heating as well.
Towel-drying
This is the tricky bit. In winter, it's easy, as the bathroom radiator will be warm. In summer it's trickier. You could leave the heating on, set the house thermostat high, and set every other radiator thermostat to minimum so that only the bathroom radiator comes on. But that would be quite wasteful. Instead, remember that you don't always need heat to dry things - airflow can be helpful too. Can you hang your towel up by an open window or something :-)
