I love starting new stuff on new shards. It's fun to be back in a place where every little bit of gold counts and every little find is awesome and useful!
To this day I can usually rack up enough startup cash turning cloth to bandaids to buy a basic LRC suit and I have yet to find a shard deserted enough (outside of SP or Mung) where I couldn't find cheap LRC suits or pieces.
Sometimes I'll start with a "looter" character. It requires nothing but time to train up Hiding and Stealth enough to stealth around champ spawns and looting gold. Even dead shards have people doing spawns every now and then and I can usually have a character looting gold in the spawns within a day.
I also train up lockpicking to the standard 95 then hang out picking chest in the Trinsic or Vesper banks while training up Musicianship and Peacemaking, gathering a lot of good stuff including gold and gems, typically easily building an LRC suit on the way as well as collecting stuff for my mule to unravel.
Mules can do normal cloth BOD's one after another by purchasing the items from the NPC instead of crafting them then selling the reward cloth back making quite a bit of profit to help get started on Tailor training.
Start a character with 49 inscription and do the inscription quest to get the Undead Slayer in New Haven. Either sell it for a couple hundred k or use it and fill it.
Start a character with 49 necro and spirit speak then turn around and get the full Necro Spellbook and regs doing the New Haven quests.
As soon as a character can cast Blade Spirit and, even better, Invis it can farm the entrance to Shame or other low-level spot with excelent results.
Always look for a rune library in Luna when you start somewhere new, I swear there is always one right outside of either the West or East gates - never fails.
Fill first four levels of spells from NPC mages.
Get that basic LRC suit up ASAP and dedicate a character to nonstop mining and/or lumberjacking.
These are all fun ways to start.