My lazy answer would be...
There's nothing wrong on picking any class to farm, even you start with smith. Yes, you would miss some times to figure out your own and zeny ratio comparing what metas usually offer. But, would you want to miss the fun figuring out how new game works instead someone spoon feeding you? It will be limited options to farm on any classes at first, but you'll open more after obtaining more experiences and gear upgrades. When you're stuck in something more specific, you could ask more or searching forum posts later.
In general term of solo farming, these classes have....
LK: more weight limit, cheaper potion consumption (but can be seen as negative, since some classes wouldn't need potions at basic farming).
Stalker: thief class have steal skill that may help your profit tremendously at some places. However, unlike other classes, it lacks of fire powers. Since, stalkers only copy attack skills without class specific's buffs or trans skills.
SG: since the limitation is too huge and very specific, I wouldn't recommend this as your first farming char. (Still, I won't stop you)
WS: way more weight limit, and it is okay class to farm, and you don't need to follow vamp smith path right at beginning. Since the skills are more zeny intensive, you can't just pick farming places in silly manner. Even mammonite is viable at beginning, for example: you still get profit when you're able to 1-shot mammonite hill wind (raw loots worth of 1.4 k zeny then minus up to 1 k cost of mammonite).
Champion: a lot more utilities, however skills are too focused on 1 vs 1, instead of Area of Effect attacks.
All melee characters have more limitation to change weapon element. You're just stuck with 1 endow for a while, and there's only few decent weapons with element to switch around.
HW: more fun to play when solo farming, even it may not be effective due to weight limit and low hp (low hp would not limit you if you could play "catch me if you can" to monsters). When you have good internet connection, you will spam different varieties of skills unlike LK, sinx, stalker, WS, and some skill combinations would give you survival on maps that you originally thought was impossible. However, you wouldn't be able to farm high level shadow element monsters effectively compared to others.
On overall advice, I would say....
Make use of tool dealers and related stuffs, anything that will give shortcuts always improve your farming. For example, using fly wing instead of walking. Speed potion like awakening potions, etc would make your attack/skill animation faster.
Use doctor (since this is private server), don't wait on your hp and sp natural regeneration. And this implies you to (almost always) spam skills unless you are in specific build -> baphomet, or berserk LK). Since skills (ex: 4x attack on bash or double strafe) often always faster than normal attack. Your farming pattern may look like this: warp portal / teleporter npc -> fly wing -> spam skills until sp or hp gone -> go back to town to refill -> warp portal again.
Read our forum guide, class specific post guides, wiki if you need more info.
Look up markets, using panel.talonro.com selling and buying shop, market channel, or forum. Learn which items people want, figure out how to farm them (check monster, map database etc, you can see monster skills on ratemyserver.net), then evaluate yourself whether you can farm them effectively or not. Using buying shop even it's underpriced, it will give you first few mils (for example: bee sting for 1.5 k) to startup any class (notice I didn't mention "entrance fee" when talking those classes). Use our panel.talonro.com database more, since our server modified some of the monsters for multiple reasons.
eden gears would be good startup equipment until you figure out the better ones. (look up eden guide)