The current setup is (TinyCoreLinux with jwm):

System: Host: box Kernel: 3.0.21-tinycore i586 (32 bit) Desktop: N/A Distro: Core Linux
Machine: System: VIA product: VT82C597
Mobo: N/A model: VP3-596B-DD Bios: Award version: 4.51 PG date: 04/18/01
CPU: Single core AMD-K6-III (-UP-) cache: 256 KB flags: (-) clocked at 367.530 MHz
Graphics: Card: Matrox Graphics MGA G400/G450 TinyCore Linux X.org: 1.6.1 driver: mga Resolution: 1024x768@60.0hz
GLX Renderer: Rasterizer GLX Version: 2.1 Mesa 7.2
Audio: Card: Ensoniq ES1371 [AudioPCI-97]
Network: Card: Realtek RTL-8139/8139C/8139C+ driver: 8139too
IF: eth0 state: unknown speed: 100 Mbps duplex: full mac: 00:10:a7:19:59:e7
Drives: HDD Total Size: 24.7GB (4.9% used) 1: id: /dev/sdb model: SanDisk_SDCFH size: 8.0GB
2: id: /dev/sda model: WDC_WD102AA size: 10.3GB 3: id: /dev/sdc model: QUANTUM_FIREBALL size: 6.4GB
Partition: ID: / size: 681M used: 14M (3%) fs: rootfs ID: /home size: 5.8G used: 198M (4%) fs: ext3
Sensors: None detected - is lm-sensors installed and configured?
Info: Processes: 86 Uptime: 14 min Memory: 44.9/756.0MB Client: Shell inxi: 1.8.17

How to make it quicker?
Use vesa instead of mga?
(its a bit hardcore to use it at the best acceptable speed with the links webbrowser)

Or another Linux? Which one?

Or use another operating system like kolibriOS, minix3 or haiku?

I just want:
- browser (no flash) in the internet
- sound radio stream
- text editor
- file manager
- ftp with GUI (like Midnight Commander)

Recommendations/comments are welcome.

You can't. Put all the PC 133 RAM that it will use into it. X with a light WM.

Browsers
Dillo
Midori with user agent set to iphone, javascript off.
elinks, dwb, lynx, netsurf

Sound
Mplayer, ffmpeg, sox, aplay

Text editor
Leafpad
vi, vim, emacs
nano, pico, joe

File mgr
Ranger, Rox, pcmanfm, mc

Ftp
ftp, gftp, FileZilla

Use flashblock addon in browser that uses flash. I +1 what teckk said. 45MB of ram at Idle in JWM from your inxi report is pretty good.

Need to do a inxi -U though to update inxi to 1.8.38 from 1.8.17.

My IBM a22m 1000hz 512MB of ram running AntiX 12 with i486 3.7.8 kernel runs about the same at idle in Fluxbox instead of JWM.