It depends how your admissions procedure works. In Cheshire (where I am) they use the Equal Preference system. So you put the school you really want your child to go to 1st choice, the 2nd second and so on. When they consider your application they look at all your choices equally - if you meet the admission criteria for a school, you get a place - simple as that. If you qualify for a place at more than one school, they allocate the school you have put highest on your list.
If you don't meet the admission criteria for a school and that school is oversubscribed, you will be allocated a place at the next school on your list (that you meet the criteria for).
Our LEA published a booklet with each school's admission criteria in - so you can have an idea of whether you meet it or not.
If your system works like this - then put your 1st choice first. If you meet the criteria (one of which is very often distance, ie., catchment - but that might not be the no.1 factor in getting into a school - sometimes it's being at a feeder primary, sometimes it's having an older sibling there. Actually I think no. 1 criterion is always Special Needs or being a child in care - but look at the list after this if this doesn't apply to you).
I would put your second choice school as second choice - because if you only put one school, and don't get a place - your second choice may have filled up with people who fitted the criteria and placed it on their list of preferences - and then, as you have been told, the LEA will simply allocate your child a place at the nearest available school.
I hope some of that helps - I think the system varies from place to place - but, if you have an admissions booklet it will tell you if your LEA uses Equal Preference - and if it does, then put your 1st choice 1st and your 2nd choice 2nd. Then if you don't get a place at your 1st choice it doesn't prejudice your chances of a place at the second - because your preferences are treated equally.
Good luck - it's such a stressful time - I nearly had a breakdown doing ds1's secondary applications this time last year