Satisfy yourself that you don't need a blade.
Once satisfied that you don't need a blade then you can start looking at bent shaft strimmers, all of which should have tap and go heads.
look for one with a two string head as opposed to one string and note the CC of the engine. Generally the larger the CC the better although this doesn't always apply.
Cheap flymo/weedeater/mcculloch string trimmers are too small/dainty/fragile and you are too close to the head. The carburettors are generally troublesome too.
Look for something slightly larger like a Homelite or Mountfield strimmer which are of a slightly better quality.
If you have more money to spend you'll find machines with Japanese engines on them but they are probably too good for what you need and they are heavier which becomes an issue after about 10 minutes of use.
Look at where the starter cord is - on more expensive engines the starter cord is on the outside of the engine rather than the inside. With the starter cord on the outside you know that the crankshaft is better supported than on engines which have the starter on the inside.
Buy from a dealer and if your dealer is any good he'll assemble it and show you it running before you leave the shop. If the carb is faulty it will generally be faulty from the start. Getting a small two stroke engine started first time is great fun especially if you don't have much experience of two stroke engines in the past.
When you purchase the machine buy a dedicated 5L Petrol can and filtered fuel funnel. Buy good quality small engine 2 stroke Oil and mix the fuel rich as this prolongs the life of the engine. If the oil is of a good quality you don't have to worry about the spark plug being fouled. If you seize the engine on a cheaper petrol strimmer you may as well throw the strimmer away as it is often more economic to buy a new one.
Is it necessary to have a mower serviced every year? I purchased a new one mid/late 2002. Can you change the oil yourself or is it more complicated than that? Is it correct to use 2 stroke oil?
This is necessary and the manual explains how to do it.
It takes you X hours to cut the lawn and you do it X times per year - do the math and change the oil accordingly.
The manuals explains practically everything you need to know about the engine and machine to which it is attached.
You should be able to do practically everything a service agent does at a service but you have to figure what your time is worth and the service agent will often spot things and tighten them up before they go wrong.
The simpler the machine, the easier it is to look after yourself.
With ride-ons or more complicated push mowers there may be known faults that the dealer fixes under warranty when it comes in for it's service.
It is correct to use 2 stroke oil in a two stroke engine which is what you'll find on most strimmers. Most lawnmowers are 4 stroke and generally use about 500ml of SAE30 monograde oil.