should use down stroke to begin the picking excercise......
in the case of chromatics.... 1234 , 1234...etc... starting with a down stroke would = down , up , down , up .... thus the next string would be started again with a down stroke.. starting with upstroke.. would yield the same results... in terms of efficiency... as the whole chromatics exercise 's purpose is to make sure your upstrokes and downstrokes sound the same.
chromatics are great for warming up and working out your picking hand. i used to pick with my pinky anchored on my guitar body... or rubbing on the guitar body... it gave me alot of stability... but i lost clarity.... due to the stability i was able to play with tiny " vibrations " ... really small movements... so i just pumped the gain and wanked really softly...
now i am doing the exact opposite..my picking hand is clenched into a semi fist.... i pick much harder now... you must be able to hear the tat tat tat tat tat of EVERY note.... if you listen to players like dhaliff , justin from allmusic ...or even mr paul daniel ...they all play hard. and you can hear every note they play....
i suffered hand aches...and even some pain ..... but it will change your playing for the better.