Can you give us some more information about your project? For example, do you want to detect DNA itself (probably impossible), or DNA oligomers (sometimes diffiucult, but can be done depending on the number of bases)?
I would just spot a matrix of 3 samples vs 3 matrices, and try out. Desalting will be as critical as choice of matrix: you can try desalting your oligos e.g. on C18 ZipTips - try desalting with 50 mM NH4OAC solution instead of e.g. formic acid - or by using NH4-loaded Dowex cation exchange beads. Look to the literature - there are a lot of protocols out there for successful oligonucleotide analysis, e.g. Ross P et al. Nature Biotechnol. (1998). A lot of these protocols were worked out for SNP genotyping by MALDI-TOF in the late 90s. Finally, use linear mode. Positive and negative mode should both work; depending on the make and model of your MALDI find a source tuning that uses relatively long delay times, to make the extraction soft enough.
I would probably vote for 3-HPA, a conservative choice that also works for larger >5 kDa oligos. THAP works better for shorter oligos, the third matrix I do not know. Re the use of amicons - try and see. They will help remove excess salt, but not necessarily the Na and K already bound, which usually is a lot. Your first spectra will show.