Does anyone have an idea about what it might be worth? And what if it were complete?
According to Bricklink, a new, unopened version of this set goes for somewhere between 160€ and 200€, although there are lots listed for double the price as well.
Of the missing parts, the 1 x 16x16 grey plate is trivial to replace, and the others can be bought for 4-6€ each (except the cardboard, it costs less than 1€) as well. This means, there is probably no great difference in the prices of a complete set and your incomplete one, maybe about 15-20€ for all the missing parts (depending on shipping and handling costs).
Should I acquire the missing parts on Bricklink to get a complete set?
That entirely depends on what do you wish to do with it. If you'd just resell it, there would be advantages to completing it, but as there are not much demand for this set and all other offers are for new, unopened ones, I doubt yours (complete or incomplete, but opened nonetheless) would be competitive without price reduction.
If you plan to use it as intended, the missing elements might prove invaluable, so in this case it would be recommended to get at least the baseplate and the cardboard.
However, if it would just serve as a playset or a parts pack, then it does not make much sense to get any of the missing parts. The blue box might be a great all-purpose storage bin, but if you need one, you already can buy any brand on- or offline. The same goes for the sorting tray.