It is best to avoid a certain mentality.
If you always buy kits, you will often find yourself getting kits that have substandard quality.
I suspect that if you were to go out on the internet and find some sort of kit that has some of the basic stuff (a tape measure, a few screwdrivers, a hammer, etc.), the vast majority of it will be junk. For example, the tape measure will probably be very dinky and buckle after being extended 4 feet. Furthermore, the handles on the screwdrivers that will come in such a kit will probably be of small diameter, making it difficult to create a large amount of torque. Should you have all of the tools that might come in such a kit? Sure. But I'd recommend you buy them separately (you might be able to get some as part of a collection, for example, a collection of 4-10 screwdrivers, but don't buy anything that has all sorts of various stuff) and toss them into a separately purchased toolbox or tool tote.
However, if you purchase power tools separately, you will miss out on all of the benefits of buying a kit. First off, power tools almost always come as (1) bare tools with no case or batteries, (2) individual tools with a case, two batteries, and a charger, or (3) kits that have multiple tools, 2+ batteries, 1+ charger, and a case or bag to carry everything.
Buying (2) or (3) will get you nice cases to protect the tools and cheap batteries. You should only purchase bare tools if (A) the tool is sturdy and doesn't need a case, and if (B) you already have an excess of batteries (e.g. 3+ batteries for every 4 tools.)
Favoring the purchase of bare tools (1), will leave you wanting cases and batteries. Favoring the purchase of individual tools that come with a case and 2 batteries will cost you a lot. Favoring the purchase of kits will leave you with a pretty good mix of tools, cases, batteries, and bang for your buck.
As Jay mentions, some cases do not come with additional space. Other cases, however, come with plenty of extra space. Ask around (friends, Amazon, etc.) or try to get a look at the case in person before buying. My Makita metal cutting saw came with a case, two batteries, a charger, and safety goggles, but there is actually room in the case for 2-3 extra batteries. The Makita drill/driver / impact driver combo kit also comes with some extra space. Though not quite as generous, it still has enough room to fit 10-15 sockets, a few hex->square shank adapters, etc. I suspect you will find extra space in DeWalt, Milwaukee, Bosch, Hilti, etc. cases as well.