Well, "self rescue" is a fairly open term.
Ropes semi-static or dynamic for use in any situation that involves live people/casualties should meet the minimum standards. These standards have been developed for a reason. EN892 dynamic rope, for example, was born out of the old UIAA mountaineering standard, ropes built to the modern standard have never been known to break, unless cut or abraded by environmental conditions.
Things to look for with a dynamic climbing rope are; manufactured to EN892 standard, full rope or half rope. These ropes are designed where a fall is anticipated or considered a possible eventuality, and the rope is bing used to arrest that fall. Full rope can be used in a single length, a Half rope needs to be used doubled.
Modern dynamics can be thin and light and still meet the standard. Thin half rope in a 60m length will provide a double workable length of around 25m depending on the length needed to construct both belays.
Article here.
A dynamic rope whilst not that efficient for hauling or climbing (climbing the rope it's self) because of the additional elongation under load, can still be used for all the tasks/uses of a semi static but has the advantage of being designed to arrest a fall, a semi static of suitable diameter, =>10.5mm, manufactured to EN 1891 will of course arrest a fall, but the faller may well be injured or killed as the semi static rope absorbed much less of the energy generated meaning that energy is absorbed by the body. >9kN impact force can cause fatal injury (=>12kN fatal) this is a problem with shot lengths in particular. A 2 meter fall on to 1 meter of semi static can generate such a injurious load.
Planning should always make allowance for suitable material that meets the standards for personal protective equipment, if a requirement has been identified.
If you're out for a jolly and someone falls off a cliff or becomes entrapped, call the emergency services. If that jolly is in a location where there is no emergency service, or the casualty is in immanent danger of expiring, use what you have but be extremely careful, especially if the material you have isn't designed for the job.
Some basic rope facts;
Tying a knot in a rope lowers the strength, MBL minimum breaking load. Generally, because tying a knot has many variables in the tying that affect the strength retained, only recognised "climbing" knots should be used, where a knot is used the MBL of the rope should be factored down by 50%. So, a 3000kg MBL becomes 1500kg.
Modern rope devices, descenders clamps etc. are designed to be used with rope of a specified diameter, identified on the individual device.
Other environmental and equipment issues can further affect the MBL of the rope, sharp or abrasive edges, belay devices and rope clamps, typically (no figure offered for sharp edges) 900kg (9kN nominal) for belay devices provided the rope is of suitable diameter to work efficiently with the device, check the spec of the device
and 450kg (4.5kN nominal) for clamps, if the rope is of suitable diameter.