I'll just add my two penn'orth to the advice given so far if I may?
Although I don't have the level of experience of many of those who have commented so far, I have learned a fair bit about fallow in the relatively short time (12 years or so) that I've been stalking.
My knowledge of the other species you mention is somewhat limited, so my comments below all relate to fallow:
I should say the main thing is to learn your deer. In many ways, fallow are unpredictable, in so far as sometimes they may be on your patch and sometimes they may be miles away. The herds are transient, within a fairly large home range, which may encompass a number of land holdings.
However, on the occasions that they are present on your ground their behaviour follows certain routines that are fairly predictable. They are quite likely to be found in the same place at the same time of day in the same weather conditions, depending also on the time of year. Learn these patterns of behaviour, and your ratio of kills to outings will significantly increase, leading either to more deer shot, or less time spent per deer.
For example, on one place I shoot, I have a highseat from where I get a view along the woodland edge to a field corner about 200m distant. If it's been a wet day, followed by evening sunshine, I can be pretty sure that if (and it's a big if) the herd is in residence, deer will emerge onto the field corner in late afternoon / early evening, presenting good shot opportunities at a distance of 180 - 230 metres. However, if it's been a dry day they won't. They will have been there in the morning instead, so a quick check of the weather forecast the day before ensures I'm there at the most productive time of day. However, if it's a full moon it's not worth going there at all as they don't emerge until after legal shooting time, and then from a different direction.
If the forecast is for high winds they emerge from the woodland edge much closer to my highseat, rather than in the field corner, giving shots from as little as 30m up to 150m.
During rain they remain within the wood, and need to be stalked on foot. If it's actually windy they'll be out in the open, lying in the lee of the wood, but again need to be stalked on foot.
On a dry, still evening that's not sunny they emerge from the wood at the opposite corner of the field, which is behind my highseat, so on those evenings I need to keep an eye open over my shoulder. Shots can be taken behind by kneeling on the seat, at distances ranging from 30m up to just under 200m.
And that's just one highseat. I have others on the same permission, each suited to intercepting deer at different times of day, in different weather conditions, or at different times of year.
And so on.
But all this knowledge is wasted if the deer are elsewhere, so I've learnt to stop and scan surrounding fields (not on my permission) using binoculars or thermal (depending on the time of day) as I drive to and from my ground, to see what's about and where. And again, I get to recognise certain patterns of behaviour. For example, if there are deer feeding or resting on a particular roadside field about half a mile from my ground at around midday, I can be pretty confident that they'll be on my ground by tea-time, and I'm ready and waiting for them.
Of course it has taken me some years to gain these insights, but I think with the greater experience I now have I could get there a lot quicker by making better use of trailcams and thermal.
It's also worth remembering that, as creatures of habit, fallow are also very quick at clocking on to predictable patterns in your behaviour, and adjusting their own behaviour accordingly. So, for example, if you only stalk at weekends you'll very soon find that the land is devoid of deer at weekends, even if you've got the landowner grumbling that he's been seeing deer around the place all week!