If one bought drivers am I correct to assume it's a single full range driver for each speaker?
How do you know when you do this the optimal size for the cabinet?
There are literally thousands of kit plans open for private use on the internet, almost all have driver lists, crossover schematics and box dimensions and quite a few have decent measurements showing on/off axis frequency response, impedance and in some cases distortion.
An example of a good, low cost solution is the Paul Carmody Tarkus - it uses relatively cheap drivers, fairly simple crossover but a fairly big box and is voiced for live music and rock, many have been built but so long as the box volumes and the front baffle dimensions are not changed then you can do what you like to the height/depth/shape. Parts for this, depending on finish would be around £500.
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I would definitely start by looking for a detailed design that has been made a few times and use that. Designing from scratch is a long education and does not guarantee good results (I'll let you know later in the year!!). If you want to have a search, designers with a good reputation include Jeff Bagby (RIP), Rich Craig (RIP), Javad Shadzi, Kurt Campbell / Jim Holtz, Paul Carmody, Paul Kittinger (for MLTL designs), Troels Gravesen (sells kits through Jantzern Audio, not free to use) and probably a few I have not listed. Many of the manufacturers also sell kits or plans for their drivers (Tangband, Fostex, SB Acoustic and Seas do).
There are a number of full range or woofer assisted wide range (WAW) designs out there but these can be an acquired taste, tend to have limited volume and take a bit of effort to get right, Mark Audio Alpair or Fostex drivers and the associated designs from Planet10 (frugel horn site) are worth a google. Another is the Dayton RS225 + Scanspeak 10F8424 design by XRK on DIYAudio that is a transient perfect design and relatively cheap to build. The pure full range need no crossover but will always have a compromise in either top end, low end sound or box size.
As always it is down to your confidence in building the box (or having a friendly carpenter) and taking the leap of faith on a design that you probably will never get to hear before building (unlike big name high street speakers) but there is the possibility, if you choose a proven design, of getting performance from a speaker costing 1/4-1/10 of the cost of a similar high street speaker (i.e. DIY = £1000 = High Street £4000-10000). An example of the DIYAudio Open Source Monkey Coffin that has a build cost around £3000/pair (and uses a very expensive mid range similar to those used in the ATC top end products) that can compete with £20k+ class high street speakers.
Choosing complementary drivers, designing the boxes (including taking into account baffle step and diffraction losses) and designing an active or passive crossover from scratch is not for the fainthearted (therefore building a proven design is suggested), there are numerous free modeling software systems and driver manufacturers publish data and curves for their products but most will advise that measurement of the drivers in the box is the only way to ensure crossover design is correct (therefore measurement mic/interface is a necessary tool).
Bit of a ramble but gives you a bit of bedtime reading / searching.