You don't say what went wrong exactly. What problems are you having? 350°C sounds about right.
I'm more familiar with the Weller equipment but the Hakko B-shape appears to be a conical tip, and the T18-B has a 0.5mm radius, so yes that's a bit large for surface mount or smaller through-hole work but typical of tips that come on irons from the factory. I prefer the screwdriver shape tips, the Hakko T18-D08 looks to be almost identical to the Weller tip I use the most. Tip size is a bit of a double-edged sword, smaller can be easier to work with, but the tiny area at the end will not get as hot or be able to transfer as much heat.
Without more information, I wouldn't blame all the problems on the tip. Be sure to keep the tip clean. I tin my tip very frequently by applying solder directly to it and wiping it in a brass-sponge type cleaner. The tip should be shiny and wet looking, even without a large amount of solder on it. This is the key to getting it to transfer heat. Don't leave the iron on for long periods if it's not being used as this just causes the tip to oxidize. I turn mine off or at least down even if I have to pause for a couple minutes.
Keep in mind that everything has to get hot enough to melt the solder, meaning the pad and the wire for through-hole components. Ideally, apply the iron to contact both pad and wire, give it a second to heat up, then apply solder to where the pad and wire meet. Sometimes it will be necessary to apply solder to where the iron meets the work. This is OK, but apply just a little at first, give it another second to heat up the wire and pad, then apply more solder to finish the joint. You'll know when things are hot enough because the solder will flow easily and fill the via.