BW have been trying to differentiate from other theme park MMOs and their "trademark" storytelling is their weapon of choice. Good or bad, if you want a good single-player experience in an MMO, SWTOR does it well. 3 friends and I were playing it over the summer, making use of the 12x XP boost to level up and it was, quite sadly, a very solo experience. We rarely crossed over, same classes had to either do the same mission twice, or seperately to advance for both players and apart from some high level dungeons (all 6 of them) which were quite well rinsed, there was little we could do together.
As a single player, you can level from start to finish pretty much solo and with little, if any, grinding. The new levelling system in 4.0 gives enough XP to level by doing just the class and planetary story missions (during 12x XP, the class missions alone were enough). If while levelling, you tried out some other things like an odd battleground, space mission or dungeon, you'll get some bonus XP and gear/rewards.
Each class has its own story, 4 per faction for 2 factions. Each class has two advanced classes for 8 altogether and the two advanced classes share the archetype's story. The stories run from 1-50 following the levelling zones/planets with frequent interludes. You'll meet your 5 companions during the story, the first on the starter planet around lvl 8-10 and the others vary considerably. The first companion (for all except the Jedi Knight) has a little more story to tell than the others and also has 2-3 missions. Each class/gender has 1-2 romanceable companions, whose decency does vary. Before, they used to have personalities and liked or disliked things you said or did. Now you can do or say anything and it doesn't matter at all.
Before, companions differed in whether they were tanks, healers or DPSers, now all are identical across the board, have no gameplay personality (only story), don't need gear or personalisation. I don't like it personally, but they're going for simplicity and they achieved it. They're great mechanically and in gameplay, letting you focus on playing how you want. I would say tho that if you're levelling solo, don't roll healer, or really even tank TBH. Both are group oriented and take longer to clear mobs and beat bosses. If you wanted to play a tank or healer, level as DPS to the high 50s, then switch over.
At 50, all characters go to Makeb. At this point there aren't 8 stories, but two, one per faction. Completing the Makeb arc will take you to or around 55 where you can do the Shadow of Revan which is a bunch of Flashpoints/Dungeons (allowing solo play) and 2-3 planets after. That takes you to 60 at which point Knights of the Fallen Empire kicks in and takes you to 65.
Regarding grinding, no not really. As I and others have suggested, you can level by doing story missions (class and planet) alone. The odd extra side mission/dungeon however is a little variety and can offer nice rewards and help keep you ahead of the curve. I know a few side missions I usually pick up for the nice, oftentimes exclusive reward or when they offer nice XP without having to travel extra distance (while I'm there anyway!). The planetary arc on Coruscant comes to mind, offering a unique(ish) and usually quite archetypal piece of orange gear that can't be had any other way.
As an addendum, my personal favourite stories are Imperial Agent in first by a large margin. It uniquely has about 3-4 distinct endings, which, unlike any other class story, *is* affected by choices made during Acts 1 and 2. A lot of players suppose (and I agree) that since the IA class was invented for this game with no basis/precedent in other SW media, the creative team behind it did a great job (the flipside is the Smuggler who gets a Millennium Falcon, a wookie companion and can marry a princess...completely ORIGINAL!).
The Jedi Knight story is probably second, tho Act 1 quite frankly should've been a Trooper story, having nothing remotely interesting for a Jedi. It did improve however. Trooper, Smuggler had a great Act 1 then mediocre everything else. Trooper picks up right at the end for a great finish...Smuggler doesn't. Consular had a crap Act I, an okay Act II and a good Act 3 if nothing amazing. The two Sith classes are utterly predicatable but moderately enjoyable in parts. Bounty Hunter is a load of utter nonsense from start to end with a few interesting parts, saved only by some fun companions and RP choices. Don't play BH for a good story, there isn't one...but you'll look very cool doing it
