Most “retail store” type telescopes have beautiful pictures of planets or galaxies on them, the implication being that one look through the “575 POWER!!” telescope will magically reveal all of these wonders with a minimum of effort. Unfortunately, that’s a long way from the truth. But you can see a lot with a small, simple telescope. The trick is in knowing how to maximize what you do have while still keeping the costs down. I've been practicing frugal astronomy for nearly 20 years - initially as a poor, just-married college grad, and a few years after that, as a parent of two daughters whose needs always come before telescope equipment. So I know how to stretch my astronomy dollars!
Fortunately, most of these inexpensive telescopes have decent objective lenses (that's the main lens of the telescope itself). They will generallycome with two or three eyepieces. If yours has a 20mm or 25mm eyepiece (is should say '20' or '25' or something similar on the eyepiece barrel), keep it. It’s probably useful, and decent. The other ones you received are likely 4, 6 or 10mm eyepieces. If those ones have “H” or “R” on them.... well - they will make a good paperweight.
Many companies sell a very good eyepiece design called a Plossl. These typically range in price from $30 to $50. If your eyepiece barrels are 1.25” barrek diameter (measure them with a ruler), Orion Telescopes, Agena Astro, Oceanside Photo and Telescope (OPT) and even Amazon.com will all have decent options from Meade, Celestron, Orion or other good brands.
To acquire .965” Plossls that either come with very inexpensive telescopes now, or better older, used telescopes from the 1960's - 1980's (and which is becoming a scarce eyepiece size), try the Antares .965" plossls from Hands On Optics. You may have to search their site for them or even Google them, as they (oddly) don't make them easy to find on their site. Alternatively, you can find some .965" eyepiece options at Surplus Shed, although their smaller eyepiece options generally aren't as good as Plossls. But they are probably better than what came with your scope, too. If you can find .965" Kellners or Modified Achromats, these are a step up from the Huygens and Ramsdens.
I recommend getting a 9mm or 10mm eyepiece of you have a 25mm one already. That, along with a good quality 2x magnification Barlow (spend $50 or more on one - it will last you forever!), will provide plenty of magnification and wide field options for most telescope focal lengths in the 600mm to 1000mm range. If you get a Barlow, avoid getting a 12mm eyepiece if you already have a 25mm one - you'll just wind up with the same magnification using the 25mm eyepiece and Barlow as you'd have with the 12mm. Get one that is longer (15mm or 16mm) or shorter (9mm or 10mm). I find the simpler eyepieces that have very short focal lengths in the 4 to 6mm range are hard to use, as the lenses are tiny and the eye relief makes it difficult to get my eye close enough to see anything.
If you have a very short focal length telescope such as an Edmund Astroscan, Celstron Firstscope 21024 or an Orion Funscope and want to get high enough magnification to see planets better, try the Zhumell Planetary eyepieces from Telescopes.com in the 3 to 6mm range or the TMB Planetary eyepieces from Astronomics.com in the 3mm to 8mm range. These are a bit more expensive, but they have good eye relief and will offer higher magnifications at reasonable cost.
Sadly, these are often the very worst part of these telescopes. The legs are often very thin aluminum if new, or soft, open-grained wood if older. The mounts themselves are often too small for the weight of the telescope put on them. And the bearing surfaces around which the telescope needs to move smoothly and accurately are rarely of high-quality machining. So if you are handy with wood, check out the website HomeBuilt Astronomy and look for the “Kid Peek Telescope” mount. I’ve built two of these for my kids, and they work wonderfully. There are also some other good frugal astronomy ideas there.
Some options for aluminum tripod owners: If you can remove a section of the ends of the tripod legs, try filling them with sand. The sand will not only provide some good mass to stabilize the mount, but the sand itself acts as a damper to vibrations.
If the objective lens (or mirror) is halfway good on an inexpensive retail store telescope, then the finderscope is probably a useless 5x24. You likely won’t see much in it, and it won’t help you find anything! One option is to replace the finderscope with a “red dot finder”, similar to a Daisy Red Dot BB gun sight. I find them a little difficult top use even under my own light-polluted skies, but for finding bright planets or obvious stars / clusters in the sky, they can work pretty well. Homebuilt Astronomy shows you how to add one of these to your scope for all of about $10.00!
The other option is to upgrade to a decent 6x30 finder. Try Orion Telescopes or Agena Astro – these tend to cost around $35 to $50 or so, but being able to see - and find - what you’re looking for in the night sky is well worth it compared to letting that $100 telescope sit in a closet unused.
Yes, I know – you’re now looking at perhaps another $100 to upgrade a supposedly “complete” telescope. I'd be upset too. But which is better: A $200 investment that actually sees the night sky, or $100 that sits in a closet because it’s frustratingly difficult to use? Better to invest $200 than waste $100, right? If you have any questions, please feel free to email me. I’ll be happy to share any insight or help that I can – I’ve probably been in a similar situation, or at least be able to point you in the right direction. I like saving money too!!