yourr tv has headphone port or rca output?
as i know you can maximize the 3k budget getting a pair of good qquality bookshelf spkr and stereo integrated amp by analog connection.
it is better than spending hdmi arc device or other half baked technology stuff

got plenty choices, hard to recommend directly. anyway i'll make it short, hopes u can catch up...

HDMI-ARC function is transfer audio data to a decoder, then play using external speakers. RCA does the same for 2 channel (left and right sound). whats make the different between HDMI versus RCA is extra ability to carry 5.1 surround.

in your case dont need surround, so why not buy speaker that able to fit on table + stereo amp. thats the best combination for sound quality.
the size is smaller and setup as easy as plug & play.

the weakness, because all in analog connection (RCA), tv has to receive all hdmi cable.
do you planning to add other video player? if true i affraid ur tv may run out of hdmi port...

the 2nd choice would be AV receiver. a.k.a. home theater amplifier with many hdmi ports. got HDMI-ARC !!
all are digital connection (non-RCA) and support latest movie codecs like Dolby TrueHD, DTS-MA and plenty more like do-re-mi-fa-so...
entry level can drive 5 channel speakers. better ones give 7 channel, network (for music streaming & remote apps), usb port and auto calibration.

it takes more space and u might wasted the additional channel because you dont plan to have rear speaker.

for speaker, need to know the depth measurement of cabinet first

it really depends what you want out of your system

3k can get you basic stereo amplifiers and bookshelf speakers. basic amps nowadays have at least 4 to 5 analog inputs which is more than enough

so newer amps can even connect digital connection direct, ie; NAD D3020 where you have optical and coaxial inputs

your source can connect to the stereo amp via normal analog cables directly or via tv (which i don't recommend)

I mentioned about ARC in previous post was bcoz someone asked what could he get for 1k.....sort off not much of a choice

speakers.....plenty choices with 1k +/- budget
in my list now....XLS Encore....local made from Sarawak......honestly speaking....kinda great sounding speaker for that price
of coz you have the usual lists of speakers like KEF, Mission, Wharfedales and etc
if you are into futuristic plus a little lifestyle wanna look fancy, KEF X300A with or without wireless is one good choice
if you are thinking into future expansions for home theatre system....you can start with a basic pioneer HT amp and basic speakers.

at the end of the day.....its what are your expectations of your sound system and what features is a must....

there's plenty of second stuffs going around....some are a bargain....

head down to few shops like Highway Laser @ SS2, Amcorp mall, Desa Home Theatre and etc.....they have packages as well

if you need to understand connectivity....let me know...be glad to help

am afraid for int amps.....i've never seen one with bluetooth or wifi capability that allows your ipad/iphone connect wirelessly.

for those stylish speakers yes....

i think audiopro might have the solution.....you can check their website

for those sound bar.......they rely on sound reflection and multi angled speaker reflection to produce virtual surround....its ok if you are not a surround fan fever
but if you are.....sound bar is not your choice

yourr tv has headphone port or rca output?
as i know you can maximize the 3k budget getting a pair of good qquality bookshelf spkr and stereo integrated amp by analog connection.
it is better than spending hdmi arc device or other half baked technology stuff

it really depends what you want out of your system

3k can get you basic stereo amplifiers and bookshelf speakers. basic amps nowadays have at least 4 to 5 analog inputs which is more than enough

so newer amps can even connect digital connection direct, ie; NAD D3020 where you have optical and coaxial inputs

your source can connect to the stereo amp via normal analog cables directly or via tv (which i don't recommend)

I mentioned about ARC in previous post was bcoz someone asked what could he get for 1k.....sort off not much of a choice

speakers.....plenty choices with 1k +/- budget
in my list now....XLS Encore....local made from Sarawak......honestly speaking....kinda great sounding speaker for that price
of coz you have the usual lists of speakers like KEF, Mission, Wharfedales and etc
if you are into futuristic plus a little lifestyle wanna look fancy, KEF X300A with or without wireless is one good choice
if you are thinking into future expansions for home theatre system....you can start with a basic pioneer HT amp and basic speakers.

at the end of the day.....its what are your expectations of your sound system and what features is a must....

there's plenty of second stuffs going around....some are a bargain....

head down to few shops like Highway Laser @ SS2, Amcorp mall, Desa Home Theatre and etc.....they have packages as well

if you need to understand connectivity....let me know...be glad to help

thats a bluetooth audio transceiver. its using the same concept as wireless sound bar u have seen, so the advantage is enable playback on better quality speakers instead of tiny sound bar.

a good quality soundbar would be the most convenient if you are not too demanding on sound quality... it would most probably look good too and won't be any worst than your TV speakers if you are into those lifestyle stuff...

HDMI ARC is usually meant for AVR in case you want to playback sound from your TV using your home theater such as using your TV to view movies via a usb hard-drive or watching astro... technically astro can also be connected to the AVR's hdmi input but that will require you to power on your AVR everytime you want to watch astro.. so, some people will connect astro decoder directly to TV and let astro's audio stream to the AVR via the TV's audio return channel...

with HDMI-ARC connected to soundbars... i think there are even certain aspects of the soundbar can be controlled with 1 single remote... not too sure on this though...

if you have a lot of external sources like a console, bluray, media player... then it's more worthy to invest in an AVR so all the connections can be consolidated into a single AVR and you have less cable clutter running around compared to a stereo setup...

you have to think of the long term setup rather than the costs you have to invest now... no point spending it than realizing you have to change your setup sometime later...

the people who would opt for soundbar are people who expects something better than the sounds coming from their tele while still maintaining some form of stylishness or able to blend it into their living area...

that is why HTIB has started to lose popularity in recent years and has grown to become tinier and tinier...

if you really don't have to dough to fork out now.. it's better to save up more than rushing into things...