How much you're willing to pay for this setup?
I can only think of Edifier S series like the S530D for the cheapest possible setup and S760D for a full setup

From your statement you seem to have 3 to 4 source (including your tv)
I think it's also possible for the R2700 and R2800 to fit your setup

or

if your tv is able to pick ALL inputs and one output to speaker that would be simple too
Edifier P3060 if you can find a cheap source to buy it
The Edifier M3400 and E3100 is no longer in production but if you can still find it then go for it

What you need, AVR and satellite speaker. done.

Audio Video Receiver, it solve your problem.

get an entry level or used. RM1k to sky is the limit...

No problem.

I don't really know about multimedia speaker nowadays.

AVR with a set of 5.1 satellite speaker system, a bit pricey but it solve all your problem.

s530d market price about 700.
u have to manually connect the speaker input signal in between devices.

AVR will simplify them as a central unit that use remote control all. higher price but more convenience functions like network play and control. a bit different sound tuning (towards movie type)
agree

passive woofer cannot be used.

actually u aim for maximum music usage or mix with movie?
i only recommend avr for mix usage. integrated amp produces much more quality at the expense of surround effects.

u can look in mudah or hifi4sale.net for good deals. experience it first then sell off and upgrade or buy new. at least u will know what sound are u aiming for and go all in for it.
dont buta2 buy later regret like i did before

i start from altec and creative 2.1 computer speakers, spent numerous hundred.
after working i bought a 5.1 sat-sub component set, 2600. spent 700 for used AVR and some cables to power them up. ok and good enough

later on get some headphones which i spent the same amount as home theater above. regreted for headfi, quit and plan to sell off slowly.

recently i bought a mini cd-amp stereo receiver. price range is expected 2k new unit include speaker but WoW its like the best bang for bucks and more (go search denon dm39, ceol, marantz melody series, MCR610 reviews and u will know).
newer model has network streaming, dlna control and support lossless codec are the best features i ever wish for. i dont even need to turn on tv.

also from there i have learned power (watts) is not all about loudness...

so avr VS stereo amp, see which route u want to go. haha

Yes you can without subwoofer at first, I started without subwoofer also but I'm using bookshlef speaker. mostly satellite speakers they come with 5.1 already.

bookshelf got better bass for bigger badder explosions??? 

it might produce more tight, clear and concise bass for music listening... but it won't be shaking your room if that is what you are looking for...

buying bookshelf first is one way of going... when you have more or enough money... you can relocate those bookshelf to become your surround or front high speakers... then get your center, main floor standers and the active sub when you have enough dough...

that, or just don't spend anything.... save until you have enough to buy the entire system... in between now and then, go and learn, look around and see what would be the most suitable for you...

there are a lot of factors when you want to invest into audio system... like room space and stuff... so, keep that in mind and don't rush into it... those are just the major components... you can easily spend a whole lot more into power conditioning, cabling and room setup...

if you are building a full blown system... i'd prefer to stay away from entry level units because before we go into features... the amount of inputs and outputs might already be a hindrance for future... but everyone gotta start somewhere right?