My advice is to not go for the big EXP, and don't melee with your pet if you can help it. Meleeing with your pet usually just means you get 2 hits in then have hate for a good 20 seconds, causing a lot of unneccessary downtime (thus killing any possible chains).
Remember, each area is different and you have to find the "flow" of it. Some areas have you charming Em's and doing nothing but slaughtering every DC-EP you can find until you make your level. Others, it's grabbing a DC-EM and taking on T-VT and getting those nice hefty chains.
I recommend going to ffxi.allakhazam.com and looking up a thread on the BST forums called "The BST Bible." Probably by far the most compiled info on BST there is.
Charming wise, it's really up to you. I charmed from level 1, whereas a lot of people say go BST/WAR from 1-12, then switch to /WHM and start lvling.
Same advice for the soloing issue. It's more or less up to you. If you are lucky enough to get someone to invite you to a party as a BST (consistantly) then go ahead and and do that. However, you'll find most times you'll still be on your ass in Jeuno when the DRG finally waltz off to their not so frequent parties.
A few tips for partying: Use a WAR sub (yeah yeah, hypocritical of me, shush) or a NIN sub, as those are more or less your best options. Some areas /WHM works, especially if you need that extra CHR boost for charming links or for getting a pet (some areas you'll actually be able to use an EM pet while exping rather than a jug).
Pre-23 you just play your BSt like you would a slightly less powerful WAR, save tanking. Just whack away at the mob and use TP for weaponskills/skillchains. Post 23 it gets a bit more complicated if you want to be good. Remember what pets intimidate what (not that it will matter, since your pet will rarely steal hate). Also, always look around before using Sic in a battle. Most pets have an AOE type move, and in places like Kazham, this can be very very bad.
Other than that, just read up on the BST forums at allah or send me a PM or two.