The main consideration is physical size. The power rating you need is less than 50 mW, so 0.1 W upwards is more than enough. Ideally, you want the best tolerance you can get, which will probably be ±1%. If you can get 0.125 W or 0.1 W, it will be easier to get into the holes, the pitch of the holes is about 7.5 mm, so a body length greater than 7 mm means it will have to stand on end.
This https://www.spiratronics.com/025w-metal-film-resistor-27r-13518-p.asp has a body length of 6.0±0.5 mm
Yes, given “terminal” software, e.g. the ‘serial monitor’ of the Arduino IDE, you can do it ‘on-line’ and save the value to EEPROM. Or you can download the sketch, modify the default and re-load the sketch. (And still do a fine adjustment on-line if you wish.)