SQLite and multiple writes

SQLite and multiple writes

I am new to databases and I'm trying to decide which one would suit my
needs the most. I am in the planning stages of a program that will store
directory references to thousands of PDF files at multiple locations (all
under one domain). Basically, all it will be is date, location,
originator's name and link to the file in each of the fields within the
database. Nothing more (no files, nothing fancy). There will be instances
where multiple writes would need to occur at the same time. I've read up
on SQLite website that only one write is supported at any given time. Does
it mean writes to a specific file or database period?
What I mean is that multiple records would need to be added from different
clients at any given time, but the existing records would not need to be
modified (and if they do, it would be done from a specific client). Would
I be able to accomplish this with SQLite or is it one write at any given
time to the entire database?
If only one write is possible, period, to the entire database, is there a
way to implement some sort of spooling system (sort of like on a printer),
where writes would wait in a queue with life timers on them?
If it's not possible, then I will look at MySQL. Cost is of a concern, so
I'm steering towards these two.