For what it's worth, as part of my job with the Saudi oil company, I reviewed (over 20 years, not all at once!) thousands of j/as from hopeful admin staff from a fairly wide number of sources. We required people to already have some five years of work behind them, but the essence of good applications is still the same, Martin.
If you're writing them by hand, make sure your writing is neat, and you check any words you're not 100% sure of before you use them. Sounds very obvious, but I always threw out the ones I couldn't read - if people can't be bothered to make their writing presentable, you figure they won't care how they do their job!
Make sure you fill in all the boxes required; explain any omissions.
Sound enthusiastic about the organisation you're applying to - better still, have a bit of research to hand that you might be able to quote, such as "I am very interested in joining Fabulous Fillies as you have the best record in producing sound milers/stayers/pink ponies" or some other reference to their business that makes them think you really ARE interested in them. (If called for an interview, don't forget to do some homework for the session.)
Include everything that might be relevant to what you're applying for, but also include additional skills (for example, computer skills and typing ability), any special interests which might be useful to them, and also in the appropriate box or space what you like to do in your spare time. ('Socializing' is usually not the brightest response, since it tells a prospective employer little about HOW you socialize - but 'learning xyz in my spare time' is very positive: employers love employees who aren't static, but are engaging their brains.)
If the forms/interviewer ask you if you're conversant with a number of items you aren't clued up about, you can always truthfully answer 'no, but keen to learn' or 'not yet, but about to read up on this area', etc. It shows you're willing to add to the sum of your knowledge, are flexible, and forward-moving.
Don't waffle! If you're asked to 'briefly describe the main areas of your expertise' then don't include every single little thing you've ever learned! You can say, 'these include, but are not limited to........' and do single-liners about each subject.
If you get a line like "why do you want to work for us?" :brows: (typical, and very typical in interviews) you can tell them that you've heard they have a good record (if you have), you know someone who works happily for them (if you do), they represent a forward-thinking organisation (if it's true), etc. Don't joke and say 'because I need the money!' If you can, put something across that indicates you have skills they might need, will be hard-working but also keen to learn, and believe that they have the necessary environment in which you can do that.
If you get to interview, and you're asked if you want to ask THEM anything, don't just say politely you don't think so. Make sure you ask them something they haven't covered, and which makes them think you've taken them seriously as a possible employer. Such as "What are your growth plans for the next 5 years?" "I'm a reasonably ambitious person and would like to work for someone who could offer me professional growth. Would you be able to offer me that?" If the answer is 'yes' then ask them "how?" If the answer is "erm, well, we were really looking for someone to just fill this job initially", then you can decide if that's sufficient inducement for you!
Good luck, Martin. It's a very exciting time for you. If I can help further, please PM me and we can natter, and won't put the forum to sleep!
Sad, but true. It may just be my lack of skill at employing the right person for a particular job, but interviewing is not a job I actually enjoy BUT in a small company we all have to be able to multi task and I got the short straw for employing new staff! 
Is going to take a long time to fill in these application forms now.