First of all, congrats on the purchase - if it's in good nick it'll last for ever. You don't say what size it is, but a little research shows that
"the 3/8" bore, No. 1 Morse taper spindle carried a 1" x 10 tpi thread and ran in ball races." This will need confirming in order to get the correct insert for a chuck.
If you're not aware, you can get chucks that will fit a specific spindle thread size, but it's better IMO to get a chuck that will accept a variety of inserts (think of them as adapters). This way, if you ever upgrade/change your lathe, you don't have to re-equip, just get the relevant new insert for the chuck and away you go.
Chucks can be a little like 35mm cameras used to be - almost identical specifications, but some small, almost cosmetic differences that attract a variety of opinions - many firmly held! I've got an Axminster Super Precision and I love it. Others on this Forum will have their own recommendations that will differ from mine, no doubt, but you should aim for a good quality scroll chuck that accepts a range of interchangable jaws.
Regarding tools, a basic set would include a roughing gouge (for turning square stock into a cylinder swiftly for turning spindles, etc. between centres), a spindle gouge (beads, coves, curves, finials, etc), a parting tool (to cut to a specific dimension, or to part the piece completely off the lathe), a bowl gouge (self-explanatory, if you intend to turn bowls) and possibly a skew chisel (for planing cuts when turning between centres).
Again, you will get differing recommendations regarding these tool sizes, but I would start with the following:
Roughing gouge - 3/4"
Spindle gouge - 3/8"
Parting tool - 1/8"
Bowl gouge - 3/8"
Skew chisel - 3/4"
You could look for a "starter set" which will probably include all of the above, although individual sizes may differ. Such sets will get you started, but remember that the sweetest cuts are made with sharp tools, so a sharpening system also needs thinking about. Of the above tools, only the parting tool and possibly the skew (if you get a flat stock, rather than an oval one) will be able to be sharpened conventionally - the other gouges will need a wheel at least.
Enough rambling - hope that gives you some idea. It's addictive, don't say you weren't warned!
Ray.