your installation steps is correct.

gapps cannot simply install. need match the correct android version.
cm10.1 is android 4.2, install this gapps
gapps-jb-20130301-signed.zip from here http://goo.im/gapps

if want to remove triangle counter, use triangle away app. its pointless tough if your warranty is over.

4.2 roms are very stable. great for daily use. here are some tips to make it better.

battery usage in settings will report very high "android OS" usage. this is a real wakelock and is a bug in all 4.2 aosp roms. flash yank kernel to fix this. you will see improvement in battery life.
http://yank555-lu.net/viewtopic.php?f=1&t=...63001beab776c5e
yank has his own forum, need to register. download "Yank555.lu-CM10.1-v1.6f++.zip" for cm10.1

when you use aosp rom, you might encounter "cant connect to camera" error.
this happens very rarely. maybe once a week. when it happen, non of your apps can access camera, a reboot is required. to avoid a reboot, install this app http://temasek.hopto.org/Samsung%20Galaxy%...tart_Camera.apk it instantly reboots the camera and makes it available again.

cm10.1 (android 4.2) already has a stable built, meaning its the last built. no more future versions for it.

if you want to install newer cm such as cm10.2 (android 4.3), it's better you factory reset and reinstall from scratch.

i did not go for 10.2.
android 4.2 aosp are very buggy for me.
all this time i was using slimbean (android 4.2)

since the default browser and camera very laggy for me on 4.3.
if you use chrome instead of stock aosp browser,
and you prefer your own 3rd party camera app, then 10.2 should be good for you.

only yesterday i start using temasek 4.4.
so far so good, browser and camera very smooth.

i just use temasek v15 with the kernel that comes with it.

from what i heard so far, i9300 has no device maintainer. codeworkx quit, and xplodewild left and started omnirom

for the past 1 or 2 month, there was no device specific fix or improvement for our phone.

all nightly were auto generated (only include very general fixes). new mali driver specificly important to our phone that were out in november was not implemented till now

i9300 did not even get a RC version. cm just suddenly put a stable tag on a random lucky nightly only.
take a look after the 'stable' version out, the following days got auto generated nightly also.

What I mean is, if u use future cm,
If you have problem that is device specific, such as camera, speaker, display or any bug that ONLY s3 is facing, it won't be fixed already. Because no device maintainer.

U guys don't notice it, but 4.2 is actually more smooth than 4.3. 4.3 until end of life still got stutter in several places that don't exist in 4.2.

Since official 4.3 release, got new sources, they were never added to cm.

Temasek takes whatever left over from cm and add in the newer drivers to temasek 4.4. But since 4.3 already  old,  neither temasek nor yank willing to add them to 4.3 kernel.

Current 4.4 is smooth with the new drivers.

i using v15.

the kernel is quite confusing actually. i also dun fully understand. here is what i guess based on past reading in temasek thread

SElinux is some kind of security, if you duwan it flash the noSElinus kernel
r3p2 mali are the new mali driver for s3. inside got 2 more kernel wolfom and beoflla something. those are sound engine.

the kernel that comes with the rom is the stock cm kernel, but added new mali driver by temasek, other than that is stock cm without mods.

since i dont really like to use custom kernel, i just use the default one.

i using v15.

the kernel is quite confusing actually. i also dun fully understand. here is what i guess based on past reading in temasek thread

SElinux is some kind of security, if you duwan it flash the noSElinus kernel
r3p2 mali are the new mali driver for s3. inside got 2 more kernel wolfom and beoflla something. those are sound engine.

the kernel that comes with the rom is the stock cm kernel, but added new mali driver by temasek, other than that is stock cm without mods.

since i dont really like to use custom kernel, i just use the default one.

Seems the Temasek v16 been plagued with sms and camera issue...

me myself having buggy camera in v15
;/

i flash d.

wow, very smooth! very light and debloated
omni latest nightly 8th december one still considered rom kosong to me. too empty and even with help of xposed framework, not my cup of tea.

temasek one kindda bloated for me. but it has been my daily driver for about a week now.
one small issue i always encounter is sometimes status bar dont become transparent (known 4.4 bug even on nexus stock rom), and another more serious one is the recent app button sometimes bring up an empty list. very weird.

cm 11 nightly is already 4.4.1 (omni also 4.4.1, temasek still 4.4)
so the status bar transparency solved (one of 4.4.1 changelog).

i hit the recent app button many times already on cm, so far no empty list appear.
cm new boot animation is very epic, minimalistic yet very cool.

guess it's time for me to leave temasek one and use cm.
surprisingly cm still got hope. not bad