I have been doing photography since about 1958.
I still have a Pentax Spotmatic and a Pentax K1000 with these I used a Bruno Werth lens with extension rings, unfortunately it was stolen, as well as a Polaris f4.5, 7 - 230 mm zoom lens with this I used a Pentax 2x converter and took wonderfull colour slides and photographs.
I now have a Nikon D1 and a Nikon D50 with Nikor lenses 18 - 55 mm and a 70 - 300 mm zoom lens. Together with this I have a Sigma 150 - 500 mm zoom lens and I also use a 2 x converter with these lenses. With digital photgraphy I have noticed a quality reduction when using the converter but not much, you will lose two f stops but that can be compensated for by increasing your ISO settings on your camera. By doing this you will increase the grain on your photograph but not as much as it was with film photography.
Please always remember that a telephoto lens enlarges the image before taking the shot but again this cannot be done infinitely. Most of the bird shots you see have not been taken with the object far away, they were still relatively nearby and then the shot was taken after much patience had been spent.
When doing wildlife photography our rule is set your camera at as low an fstop as possible and then on aperture priority, the camera will select the correct shutter speed for the shot.
Also another simple rule rather over expose a shot slightly as this can be corrected when editing the shot without risk of increasing noise, should you underexpose you will always increase noise white brightening up the shot. I always take at least two photographs of my object, one with the suggested shutter speed and one with the next slower shutter speed in other words I set my bracketting accordingly.
We have had great success with with what I have mentioned above.
Furthermore when purchasing a lens get a zoom lens, they are much more suited to wildlife photography, also save a bit longer and purchase one with "vibration reduction" and auto focus
this helps a lot, most poor photos are due to camera shake, use a bean bag resing on a wall or a car window for thye stability of the camera and lens.
A bit of advice - do not buy something now what you really need, if you cannot afford it yet, rather save a little while longer and get the best for your requirement as buying now and improving later is not good economics.
Very often you can get a very good quality second hand lens at a reasonable price, check it yourself let it be checked by a reputable person, if necessary have it serviced by an institution that is qualified to do so and enjoy your photography.
We will be looking forward to your shots in future. Also remember practise makes perfect and also that not every shot is the ultimate if you get more than 15% real good shots - you will be doing extremely well.