honda/acura seems to be a outlier in the sequence, most vehicles it's furthest to closest, (RR, LR, RF, LF) rather than closest to furthest (LF, RF, RR, LR) why I don't know but that's the sequence. I'll best most any indy and many dealers do the RR,LR,RF, LF sequence since it's so common.
IMHO brake fluid is so inexpensive there is no reason NOT to use a DOT4 fluid instead of DOT3. Just don't use a DOT5!!!. And even among DOT4 look at the wet and dry boiling point. some are much better than others with noticeably higher boiling points and moisture absorption rates. I've been using the Valvoline synthetic DOT4 in all my vehicles for decades. And I have a motive performance pressure bleeder so I just suck out fluid from the master cylinder, refill with fresh fluid, hook up the pressure bleeder and bleed till I get REAL clear fluid from each caliper. May take a little more fluid, but again, it's inexpensive enough to not be an issue. I generally use 1-1.5 qts on cars, 3 quarts on my pickups with larger calipers and longer lines. Always have an extra quart on hand if needed.