A soft or medium brush with a small head reaches the back teeth and the gum line better than a big, hard one. Hard bristles do not clean better; they wear the gum and the enamel near it.
Electric or manual both work if you brush for two minutes, twice a day. Many people find an electric brush with a timer makes the two minutes easier.
Replace the brush, or the head, every three months, or sooner when the bristles splay. Ask the hygienist at your next visit to check your technique on the places you miss.