Assigning a Unique Number to a Row

Greetings,
I saw this discussion once before but can't find it now.
I'm looking for a way to assign a unique ID to a new record without using the 'auto-increment' function of MySQL.  I considered having a one-record table with fields <last_cust>, <last_mbr>, <last_order>, <last_item>, etc. and upon 'submitting' my new record form data, first go and get the <last...> simultaneously adding 1 to the old data (or add 1 to <last...> then subtract 1 before adding the new record.  I suspect I can't do this with one query thus leaving the possibility of simultaneous overlapping queries from 2 users.
By simultaneous overlapping, I mean:
User 1 executes the increase by 1
User 2 does the same before User 1 retrieves his/her updated value
Possible? Suggestions?
Thanks in advance.
Tom

bregent, shocker:  Thanks for replies.
My concern was that when using an auto-increment for my membership and inventory files I would not be able to capture the new 'id_nbr' without a query based upon the inventory description or member name.  The inventory display page, especially, needs to be able to show a photo of the item (maybe also a member photo on the membership page!).  I thought that if I could immediately capture the new item/member id_nbr, I would not have to cycle too far to present the opportunity for user to upload the photo and the photo file name would be the same as the id_nbr (make sense?).
bregent:  With the possibility that my (or a future host) won't support 'isolation', I'll probably not look at this; However, your suggestion on table format makes sense, so thanks.
While awaiting a reply, I considered writing the 'session_id' to the membership and inventory file(s) as the new record is added.  Since I have it ongoing thru pages as the user proceeds, the page to upload the photo could have the session_id as the getRecords query WHERE CLAUSE thus ensuring they only get 'their newly added' record.
Tom

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