I looked at the kit you are considering, and I gotta say that it doesn't look like a bargin to me. The lathe tools will get you started, but you will quickly outgrow them and probably never use them again. Invest in a couple of full size tools and you will be happier in the long run. Slimline kits are cheap, and you can get an assortment of finishes instead of just 40 gold and be happier. You already seem to have a supply of wood, so the blanks are no bargin for you. you will need a mandrel and pen mill, but can get those elsewhere for small money. Glue and sandpaper are also available easily and not expensive. I recommend getting a 2 oz bottle of all 3 types of CA and some accellerator from Monte or somewhere, this will help you glue in tubes, stabilize and repair woods, and finish pens once you get the hang of it. that really leaves the assembly press as the most expensive part of the kit. I've never had one, so I may not know what I'm missing, but for what you end up paying for that one, you can buy yourself a decent drill press (or a good used one if you can find it used). Turn a small press pad to put into the chuck, and put a piece of flat wood on the table, and use that to press pens together, and drill your blanks too. You will need a drill press eventually, might as well get it to start. I will add that I consider a good hardened 60 degree livecenter an absolute necessity to make your mandrell run true. and while you are getting that, get a dead center too. For less than ten bucks, even if you don't eventually turn pen blanks between centers it's usefull to finish between centers or use it to round down irregular blanks to be drilled.
Most of these items can be purchased from members here at or below retail, and if you mention that you are just getting started buying your initial turning kit, will probably come with some freebies to make shopping and turning more fun.
Of course, all this is just my opinions, and may or may not work best for you. Depending on were you are and what tools you have to start with changes what's available. Given that you are here before you even got a lathe, I think a little research will stretch your startup money and get you further than a one size fits all kit.