When you purchase a new telescope (or even a secondhand one) it will normally come with some eyepieces.
The ideal thing to do is ignore these and purchase yourself a set of Naglers or similar. I would suggest at least a high, medium and low magnification at the very least. These can be purchased here.
I will assume most of you have quickly walked away empty handed. If not then you do not need to read any further. I hope they are really worth it and I get to look through them at our next meeting.
I am going to make an assumption that the first scope you purchase is going to be 8" and below.
Even small cheap scopes can be improved with a good quality eyepiece. I would say that Plossls are going to be the best value for money. By purchasing a branded Plossl you should end up with a good quality eyepiece with good viewing over most of the field of view (fov).
The faster the scope the harder the eyepiece has to work. Plossls normally fit the 50-52° so should be more than reasonable. Ideally only 3 or 4 eyepieces should be needed and as mentioned earlier a high-power, medium-high-power or meduium-low-power and a low-power.
If you find the ones that came with your scope are marked 'K' then you should find these will be acceptable but will have a smaller fov of around 45° if they are 'H' or 'SR' then they really should be upgraded.
Now for some maths
If you multiply your focal length by 3/4 this will give you the size of your high power eyepiece.
A scope at f/10 x .75 will give you 7.5. This should allow you to use your scopes magnification up to around 2/3 and a respectable view.
If you have a f/4 scope then this would suggest your maximum eyepiece should be 3mm. This may end up being a disaster and very difficult to use. For a faster scope (f/5 or below) then use f/ x 1.5 and a good quality x2 barlow to achieve your high and medium power eyepiece (ep).
Now multiply your focal ratio by 1 1/4 for your medium-high eyepiece.
The medium-low use f/ x 2.
The low eyepiece is worked out by f/ x 3.
For a faster scope you will be looking at and eyepiece of 3 to 4 times your focal ratio for the medium-low and about 5 times for the low-power ep.
So far we have a rough guide.
f/8 6, 10, 16 and 24mm.
f/10 7.5, 12.5, 20, and 30mm.
f/5 8, 18, 25 and 2xBarlow.
If your wallet will not stretch that far then for planetary/lunar you may wish to ignore the medium-low ep and if you are going to view dso's then maybe think about losing the high power ep. Although you will have times when you will be looking for the high power ep.
A dobsonian mount will differ in the way that at high magnification of around 200x it get very difficult the keep the object in your fov and you may spend most of your time trying to get the object back. This will improve with practice.
I would recommend that you have no more than 200x magnification and 5mm exit pupil. This works out that a 10" f/5 dob will have a focal length of 1250mm. A 6.25mm ep will get you 200x so about a 6.5mm for you high power ep. For your low power you divide your aperture by 5mm (exit pupil) to give you 50x and a 25mm will be needed. If you are younger then you would be better with a 7mm exit pupil. This would be 250mm(10") divided by 7 = 36mm so a 35mm eyepiece.
You can then fill in the gaps between. Maybe: 6, 10, 16, 25mm or 6, 12, 20, 35mm.
If using a 8" f/5 dob then maybe 5, 10, 16 and 25mm
To work out the magnification of an eyepiece then you divide the focal length by the size of the eyepiece.
To work out the focal ratio then use focal length/aperture.
If your still awake and have made it this far....Well done!!!!
Please do not feel that you need to rush out and replace all your eyepieces, after all its better to have something than nothing. Remember that eyepieces are a real minefield and the best option is to try before you buy if possible. Take your time, check out the second hand market places and most of all enjoy the views.