I do long distance self supported road riding. For this style of event you need to be able to carry luggage and having fenders (we call them mudguards in the UK) is an advantage
If you look on my website http://audaxing.wordpress.com there is lots info on this type of bike
If you want to exclude the heavier sort of bikes (touring bikes, 29ers with drops, Surlys) then there a few other options
There are three possible solutions to this problem, based on three types of bike. The types of bike I'll try and explain are a "winter trainer",a "adventure bike" and a "standard racer"
A winter trainer is (I would guess) the type of bike that your Dad had. I have a Ridley Aeron that is this type of bike. It has mudguard eyes, rack points but it only allows narrow 25mm tyres with mudguards. It has rim brakes, not disk brakes. Weight wise it is about the same as a "standard racer" made of similar material. My winter trainer is aluminium but steel is also a common material. Pricewise they tend to be cheaper and if you buy it built up into a full bike it will have lower end components. I built mine up from a frame and it has 38x48 chainrings and a mtb 11-34 cassette
The Adventure bike is the latest thing from the marketing depts of the bike industry. Also known as a gravel bike this is a fast road bike but with some touring bike, cross bike and MTB features. They have tyre clearance for large tyres - which are comfortable on long distances and usually have mudguard eyes. Strangely, not all of them have rack mounts because there is also a fashion for attaching dry bags with velcro (so called "bike packing" luggage) instead of using racks. These tend to be as light as a compariable "standard racer" but somewhat more expensive. They also always have disk brakes. I have a built up Genesis Datum 20, you can see the spec on their website. It has wonderful SKS longboard mudguards with 30mm tyres
Finally there is the "standard racer". This is just like the bikes on the Tour de France. It is super light, has no mudguard or rack points. To fit mudguards on these bikes you use special kits with metal p-clips to attach standard mudguards or you use clip on mudguards. The best type of clip on mudguard is the Crud Roadrace. These are full length, fit any racing bike, has excellent coverage but don't last very long before falling to bits.
If you really want to fit a rack to a "standard racer" or a "adventure" bike then probably the best option is to attach a seat post mounted rack
If I want to carry a lot of "stuff" on a racing or adventure bike with no rack mounts I would use a saddle bag and/or a bar bag
Hope this information helps