Lulz, im an i9500 user   Not for i9505

Last time I tried downloading my I9500XXUBMG1 for THREE days and nights before getting it, was so frustrating.  You can try using different browsers, some browsers can pause and resume the download, you can try it to revive the download when it seems to be dead.

maybe you can be a bit more specific as to what you need in a custom rom. basically there are 2 types of rom available for the S4 lte. Touchwiz aka stock samsung-based ROM or AOSP-based ROM (Google Edition, MIUI and etc).

if you're not sure what you want I would suggest you try the TW-based rom with minimal mods but custom kernel such as wanamlite or goldeneye roms. understand that stock roms with less mods are more stable and reliable which is very important. Roms with lots of mods such as echoe, x-note, phoenix will give you more options to customize but make the rom less stable/reliable.

but if you want something totally different then try the GE roms for the full Android experience. AOSP roms are very fast and smooth but you may lose some hardware features such as sensors and LTE.

hope this helps...

Ive mentioned earlier, avoid MIUI. In my opinion, it is loaded with tons of bloatwares and wakelocks.
Ive tested for 3 devices already and all results the same.

There's a MIUI thread in XDA for I9505. I've tried the official one for I9500.  Most of the time it's nice, but the battery ain't great, SOT 2+ hours if lucky.
Otterbox Defender got flip casing?

Actually i have no idea about i9505 but ive been lurking for a while in their thread.

I cant find any minimum mod-ed stock rom based, but i think this one you can give it a shot.
http://forum.xda-developers.com/showthread.php?t=2639202