For prototypes with through-hole components, frequencies < ~40MHz, stripboard/veroboard is just fine.
The stripboard layout lends itself very well to designing a PCB, with strips going on one axis, and components (usually) going the other way. Tracks can easily be cut, and jumpers/wires added anywhere you wish. Very easy for DIP packages (jumpers can go under chips too!). You can even use SMT passives, 1206/0805 resistors and caps on the underside. Whilst theres the classic 'strips' you can also get 'tripad', which is just stripboard with cuts between holes every three holes. Saves cutting tracks, can can mean lots of jumpers to make 'long tracks', ones that are more than 3 holes long (line power/ground lines).
As most stripboard/veroboard is made with crude FR2 paper substrate, it may not be fully robust and not ideal for medium frequencies signals, but its very easy to cut/machine/file, its cheap, and I have tons of the stuff. Holes in these are usually 'punched', rather than drilled, so they might not be perfectly aligned, but generally good enough for anything. You can of course get FR4 stripboard, more expensive, but much stronger, and as the holes are 'drilled', they are generally very precise and clean. Better for higher frequency signals. These are often tinned as well, for extra durability as theres no bare copper to corode. My colleague uses this stuff exclusively for prototypes because he says it looks more professional, and won't warp/break in industrial gear.
For > 3/4 circuits, or with extensive SMT components (such as SOIC, SSOP, DFN etc..) then having a PCB made is much easier and cheaper in the long run. For prototypes you can add extra pads, tracks, footprints and 'cutting tracks', to your design to make modification easier. Often my first prototype, if there is any spare board space, it will be filled with these, as well as 'double footprints' which give one the option of using the same part with a different package. Test pads are also handy, especially if they have holes, so wires can be inserting for testing, or external modifications like adding a smaller board for corrections.
There are many half measures, between pure stripboard, and a full double-sided PCB with silkscreen and solder mask. These include using stripboard, but with SMT adapters, or prebuilt modules (I must have around 200 breadboard modules for this..), to single sided DIY PCB's using toner transfer, all the way to manufacturer prototype PCB's, that have no silk screen, no solder mask, and basic outline routing. The last tend to be fairly cheap and avilable in smaller quantities than full PCB's.
Depending on complexity, application (is it going to be shaken about?) and parts usage, if you can, I would just go with stripboard for a proof-of-concept. You can go from an idea, to a schem to a working board in an afternoon, then have more time to make modifications to the circuit based on measurements. parts can easily be removed if needs be for the next prototype, meaning you've only spent a couple of bucks on the board itself. Next up after that would be a quick prototype service.
DIY PCb's I can only recommend if you make a LOT of one-off's which have some SMT (less holes to drill) and applications where frequency, power, and size are strict. I've made many, its always a pain drilling, cleaninge etc.. so as a 'half measure' I often make modules for SMT's, with a bulk of awkward circuitry, broken out to 0.1" spaced pins to solder onto stripboard which can be used to add standard pitched through-hole devices.
Its always good to take pride in ones work, to admire the finished board. I have seen some shocking prototypes that have worked wonderfully but look awful, and were almost impossible to modify. If you have space on stripboard, space things out, add test points, reserve area's if you think you'll need some extra circuitry in there, and whilst it won't be small, or perhaps good looking, it'll serve you well until you're completely satisfied with it.
Probably said too much there... but I've been prototyping for half my life