So, standard advice before tearing into this:
You should make a full system backup to an external USB drive. If you don't already have one, you can purchase a 1 or 2TB drive inexpensively. You should continue to back up your system to the external drive on a weekly or monthly cadence. When not using the drive for backup, it should be physically disconnected from your computer and powered down. This provides you with some protection in the event of a cryptolocker style infection. Buying 2 drives and alternating backups is even better.
The free version of TreeSize is worth pulling down to see where your space is being used.
http://www.jam-software.com/treesize_free/
Depending on the migration software you're using, you may also need to use a bootable partition resizing tool. GPartEd is one option, there are many. You should make the partition as small as feasible for your remaining data, you can inflate the partition to full disk size after migration via Windows disk management.
http://gparted.org/livecd.php
You should still upgrade your RAM. Assuming your current RAM is in a sane configuration, you should have 2x1GB sticks and 2x2GB sticks. I'd suggest buying 2x4GB sticks and putting those in place of the 1GB sticks. Buying used is a good option here. There should be a lot of working pulls available as newer systems for the past couple years are on DDR4.
The Samsung 850 EVO Thunderbolts mentioned is a great go to for price/performance. Looks like Amazon UK has those for 89GBP for a 250. A 500GB drive gives you a bit more breathing room and either of these can be migrated forward to a new desktop. Laptops would be more hit or miss because more and more laptops are ditching the 2.5" drive bay for M.2 slot only.