* Astronomy

How may eyepieces should i start off with?

Telescopes generally come with two or three eyepieces and sometimes a Barlow lens. But three or four good (perhaps Plossl design) eyepieces of various wide ranging sizes, 6mm, 10mm and 25mm, and a quality Barlow lens would be my 'starters' recommendation.

The eyepiece sizes, or eyepiece focal lengths, would really depend on two main criteria; the size of the objective or mirror and the focal length of your telescope.

A common 'fast' f5 114mm reflector will have a 4½" (114mm) mirror and a focal length of (about 5 x 114) 570mm. The maximum magnification will be dictated by the size of the mirror (50X per inch), which would be ~200 times magnification (the reality is that, seeing, light pollution, optical flaws etc lower this figure to around half, This is particularly relevant in fast refractors, without suitable colour correcting filters.).
To get a useful number for a high powered eyepiece we just divide the focal length (570mm) by ~200 (or better ~100) to give the focal length of the high powered eyepiece. The figure works out to be 2.85mm, or if i use the more realistic 100x, then 5.7mm.
So a 5 or 6mm eyepiece for high power on a f5 telescope (It should be noted that i can recreate this number with a 10mm or 12mm eyepiece and a 2X Barlow).
A 10mm eyepiece will give ~60x magnification, (enough to start to clearly see the bands on Jupiter). A full moon or solar disk will almost fill this eyepieces field of view.

For medium power a 16mm, 17mm or 20mm eyepiece will give nice results (for 35X to 28X magnified views). Depending on the field of view, the moon will fit quite nicely in this size of eyepiece without the need to constantly nudge the telescope (with those without motor drives). And at ~30 x magnification the detail on the lunar surface really starts to become interesting.

For low magnification views the limit would be ~30mm, but a narrower field of view (40°) 40mm would be quite acceptable, for 19X to 14X  magnifications, (note that i can recreate a ~16mm eyepiece using the 30mm and a 2X Barlow).
This very low (and seemingly useless) magnification will help in navigating your way around the sky, and to some extent help in seeing very diffuse objects like comets, nebulae, etc. However, a lot of light is physically lost as the exit diameter of light will be larger than the pupils of most peoples eyes.
A nice compromise would be a 25mm eyepiece (which is quite a common size to be included with telescopes - and if used with a Barlow will give a very useful 12.5mm eyepiece). A nice Plossl (52°) in this size will frame the Pleiades or Hyades.

The low-down is that you probably already have these sizes with the telescope.
If you are on a budget, there is no need to invest in other eyepieces (other than a really good quality Achro or apo Barlow lens replacement, if you have a cheap single lens barlow).

Personally, I would invest in individual lenses rather than use Barlows (as putting anything in the light path is going to degrade it). So a 5mm, 8mm, 12mm, and 25mm would be my 'seasoned observers' choice selection on an observing night with a portable fast  telescope.
(Of course, if money, or room or weight allowed, a 4mm, 6mm, 10mm, 17mm, 20mm and 32mm would fill in the selection gap quite nicely).