You can play SWTOR for free as it's now free-to-play but you will be restricted with things... You wont be able to carry as many credits, you'll have fewer character slots, limited in raids and things like that, you wont be able to send items, and there are various other things you wont have access to. Basically, with free you play the story missions and that's it. You're so restricted here that it's not much fun in the game.
With preferred status, which is after you spend a certain amount in the cash shop (with real money) you get access to a few more things for the lifetime of your account. You don't need an active subscription, you just need to have made a purchase in the shop ($4.99). You get slightly higher priority in the login queue, your bank can hold a little more credits, you can run a few more raids per week, and you get access to a few more things. But you're still pretty limited as to what you can do, you still have quite a few restrictions but not as many as a completely free player.
With a monthly subscription, of course, you get access to everything with no restrictions. You also get Cartel Coins every month to spend in the cash shop. If you really enjoy the game a subscription is probably worth it.
If you've never played the game before I would just start out with a free account and see what you think of it. SWTOR is a game where you either really like it or you really don't, there's not much of a middle ground. I was a head-start veteran and played for about a year before I got so bored with it that I couldn't take it anymore. But that's just me, I'm not really into PVP or raiding and that's pretty much all there is to do as max level. Well, those and extremely tedious daily quests. I hop in every once in a great while as a preferred player (I'm preferred because I used to be a subscriber) and poke around a little bit but not too often anymore...
That said, I have a level 55 Scoundrel, a level 50 Jedi Sentinel and a level 35-ish Sith Assassin on Begeren Colony. Heh.
By the way, on that page of the status breakdowns, if you scroll over the little circle icons it will display an explanation of what each benefit/restriction is.