Brought up in Shirehampton and have sinced lived near Filton, Avonmouth and now Sea Mills.
Depending on your house budget I would say the following:-
Sea Mills - near the Station is pleasant but pricey (residents call it Stoke Bishop!)
Sea Mills "proper" ranges from half a mile to a mile away from the station and is a mixed ex council/private estate and can range from good to rough! A typical 30's semi goes for about ú180,000 (brick) or ú160,000 (Reinforced concrete)
Shirehampton around the station ranges from a row of about 40 3 bed late victorian terraces at about ú150,000 through 30's semi's at ú180,000 to some nice riverside 70's properties - 2/3 bed bungalows/small houses.
There are a group of late georgian properties by the river in station Rd that are probably ú250K plus. Also a small mews of 15 or so 1990's 2 bed bungalows too. A lot of upper Shirehampton, like some of Sea Mills can be a bit rough too.
Avonmouth - which I like a lot - has a good community spirit but suffers from an old reputation of being the old docks area. I believe it will come on leaps and bounds as the village high street route to the docks has now been bypassed with a direct route to the motorways. It is mainly victorian terraces but some are substantial. Prices ú140 - ú220K.
My Bro has lived many years in Portishead and now Clevedon - but no trains!
Worle in WsM might be worth a look?