don't use a direct debit for oil tank. keep a check on the level - the standard gauge will do (no need for gadgets) but you MUST pull out the valve on the bottom to see the actual level. As others say, don't let it run dry but if you can organise not running out of knickers you can organise not running out of oil. It is not a job that requires a Y chromosome. Oil heating generally cheaper to run than gas, although you will pay a bit of a premium on your electricity without the dual fuel discount.
oil theft is pretty rare but check that you have insurance. Don't lock the tank, all that will get you is a hole in it.
boilerjuice is a good way to track prices but they charge a premium, so find a good local supplier. Price has gone up a bit since the recent low but is still good, so tank up as soon as you move in. There's no rhyme or reason with prices and seasons, and it isn't related to petrol price either. Boiler MUST be serviced annually by someone OFTEC registered, ask who the neighbours use. Get it done in the summer.
if it is a really old boiler it will guzzle oil. As VAT is charged at full rate on replacements it will take about years to pay off, but it is worth doing especially with a probable no-deal coming and the resultant massive inflation. This is a summer job though and you may struggle this year.
septic tank; same as normal sewage, nothing goes down the toilet except body waste and bog roll. Nothing goes down the sink except washing up water - same as mains drainage. You can't have a sink waste disposal (nasty environmentally anyway) and make sure no coffee grounds go down, little pellets clog the tank. Also means you must use washing liquid not washing powder, this will knacker up your washing machine in a few years so don't buy a pricey one. If you are a type that chucks bleach down sinks and toilets, time to stop - pointless anyway. Clean bathroom with normal stuff, a bit of bleach on surfaces doesn't hurt but tipping it down the toilet is ridiculous.
HOWEVER with a shared tank you've no control over what others do, so expect to be paying to empty it yearly or more often. Our private one needed doing after 7 years because we don't use bleach beyond the tiny amount in the dishwasher tablets. Find out who does the emptying because when it needs doing, it needs doing quickly. Check beneath manhole covers occasionally. You pay less on your water rates because no sewage element.
other no-nos are dishwasher and washing machine cleaner. Although you can do what we do, disconnect the drain hose outside, run the cleaner, let it empty into a bucket and chuck in a quiet part of your garden.
good point about spreading out washing machine use, depending on how good your drain field is. We get a bit of a puddle if the machine is used more than 3 times in a day, which is pretty rare.