If the bike is all there, I would suggest new cables and cable casings. New brake pads. New handlebar tape. New tires. That should run between a hundred and two hundred dollars, assuming that you can do the work to install the items mentioned.
The other big issue is lubrication. Grease, left to sit for a long time, can deteriorate. More than once, I have opened a bottom bracket to find rust colored dust and nothing more, except, perhaps, a forest resident...
Take a really close look at your front derailleur, assuming it is the stock Simplex Competition model (this applies to all Simplex plastic front derailleurs), as they have a reputation for failure. As often as not, the crack will appear here and, if a wee bit cracked, will snap completely during assembly or shifting or...
The PX10 is an iconic road bicycle, that offers a really decent ride quality and looks horribly good doing so. Two have come my way, over the years, the one pictured left home last summer when I did an N-all but two...