Easiest image site in my opinion is Imgur. Create an account if you don't have one, then drag and drop your images in. If you then click on the image, you'll get a list of pre-gen links you can use, and at the bottom right is a selection box for sizes. I've given examples of small/med/large thumbnail here:
https://imgur.com/CbgvpAX
https://imgur.com/pM1Zx9S
https://i.imgur.com/3ZCE23NI recommend including the direct link as well, so people can view your images in all their glory and full size.
Use the "BBCode" image tag (5th one down, 2nd up in the link list) and just paste it in here to embed the image like above, and it'll work on this forum.
Also, for those looking for a quick, easy, and frankly gorgeous resulting ship builder, as Marcus notes, I'm a huge fan of Galactic Civilization's shipbuilder (I'm using GalCiv3). Game is great on its own, but the builder makes ships like these take minutes instead of hours or days. I'm planning on having ships for each of my designs eventually. All of the above designs are from GC3.
Oh, and some tips- Options, use all parts lets you use any race's ship parts. The XYZ tool is useful at times, too. But the most useful tool is the ability to select a set of parts, save them as a whole, and use them... Including in other ship designs. Build your Dropship, then import it in for dropship mounts on your ships.