should i import my char from the shadows of siege of shadowdale to crimsons tides of tethyr to darkness over daggerford? or i will be overpowered?
No to the latter, Darkness over Daggerford and Crimson Tides of Tethyr run over the same level range, you'd be severely overgeared and overleveled. The thing you want is Tyrants of the Moonsea.
Siege of Shadowdale, Crimson Tides of Tethyr and Tyrants of the Moonsea form a "soft" series, meaning there's a common core plot thread running through them, but they can be played with either the same PC or multiple, independent ones. Each module has a seemingly standalone central plot, but they share an underlying conspiracy which pops up in various aspects.
Alternatively, you can take a Darkness over Daggerford PC into Tyrants of the Moonsea, that's also explicitly supported. Either way, it's just flavour and it comes down to one or two conversations where you may identify yourself as the hero of Tethyr, the hero of Daggerford, or reject any connection altogether. CToT's resolution does offer your PC a chance to "retire", story-wise, so you could do SoS and CToT with one PC, then do DoD and TotM with another PC. The levels are matched either way, both CToT and DoD should see you to level 14 and the default starting level for TotM is 15.
also what type of melee weapon is best represented in the trilogy? i was thinking of swinging a greatsword.
That's a bit harder to say, I'd probably pick Longsword as the most prominent across the different modules. For my part, I'm playing a DoD -> TotM run right now and I picked up a cool Greatsword in the former module, it's working out beautifully. If you're going all the way through TotM, you'll get an opportunity to upgrade any melee weapon to a +5 and 1d8 damage bonus of your choice, so it's other special properties, like Keen or stunlock stuff, that are going to make the biggest difference.
So it depends on what you wanna take into TotM. If you're going from CToT, that's got one or two beastly Longswords to be had and I also seem to recall a nice Greatsword. If you're going from DoD, that's also got some nice Longswords, but you can also get your hands on a Keen Greatsword or a Keen Scimitar for crit munchkining. There's other options across the series, Bastard Swords, Warhammers, Flails etc. but I think the prior ones might be a bit better represented.