Mechanics of Chromosomal Crossover
How does the cell select where to to make the break on both chromosomes? 


There are proteins that direct the selection of a site where a double strand break will be made on one chromatid. 


  Crossovers are not randomly distributed: The histone methyltransferase PRDM9 recruits the recombination machinery to genetically determined hotspots in the genome and each incipient crossover somehow inhibits formation of crossovers nearby, a phenomenon called crossover interference. Each chromosome bivalent, including the X-Y body in males, has at least one crossover and this is required for meiosis to proceed correctly. 
  Credit; Reactome


.


  Is it based on some attempt to match sequences on the two chromosomes, or purely on distance from the centromere? 


The sequences are matched but not as you have assumed. Following the introduction of a double-strand break in one chromosome the regions around the break are processed (by proteins) and these processed ends invade the opposite chromatid. The formation of a Holliday junction follows, these are the "X" structures between strands in the image below, and they requires base-pairing; 



Image credit; EMW2012