happy-the-monk already named a good option with rsync. I am just going to throw another one into the room. Perhaps it will be of some help to you. My proposal will however compress all files, no matter the size.
I like to copy files using the combination of tar and ssh. Like that you just pipe one big bytestream through your connection (and you can transparently add compression). If all the files you want to copy are in one directory (and no others), you could try the following:

tar czf - SOURCE_DIR | ssh USER@REMOTE_HOST "cd REMOTE_DIR; tar xzf -"

# or if the tar is sufficient on the other side:

tar czf - SOURCE_DIR | ssh USER@REMOTE_HOST "cat >REMOTE_DIR/backup.tg
+z"
[download]

In my experience the combination of tar and ssh is much faster than scp if you are copying many small files. If your system is more current, your tar might also provide different compression methods like -j or -J:

     -j, --bzip2
           filter the archive through bzip2

     -J, --xz
           filter the archive through xz

     -z, --gzip, --gunzip --ungzip
           filter the archive through gzip
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bzip2 and xz will usually reach higher compression levels than gzip. They require however more cpu and ram, and the compression will be slower. In my experience one can achieve the highest compression with xz (-J). If space/bandwidth matters more than (cpu-/real-)time and RAM, you might try stronger compression methods. For most cases gzip will however also be good enough and quite fast.
If you just want to copy a few selected files from random locations you could for example create a file with the filenames and then pass it to tar using -T:

     -T, --files-from FILE
           get names to extract or create from FILE
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To skip files, use -X:

     -X, --exclude-from FILE
           exclude patterns listed in FILE
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If you want a graphical progress you can combine it with pv (you might have to install it first). E.g.:

tar czf - SOURCE_DIR | pv | ssh USER@REMOTE_HOST "cd REMOTE_DIR; tar x
+zf -"

# or if the tar is sufficient on the other side:

tar czf - SOURCE_DIR | pv | ssh USER@REMOTE_HOST "cat >REMOTE_DIR/back
+up.tgz"
[download]