I use a magnifying glass to check my cuts, then use a meter to make sure there's no electrons creeping across.
For the joins I've found that the inner core of old tv aerial cable is perfect.
I also use that to secure wires attached to the edges of the board. I sling a little loop over the wire, through the hole, pull tight then solder it on the back. It does mean that whatever any diagram shows as the board size needs to be a bit bigger to facilitate the connecting wire to pots and switches, jacks and so on.
Don't forget that if you plan to use the old stereo jack switch trick then you need to have a spare track for the battery ground. So all grounds to their track, battery to this spare (edge) track and when you put the TS plug in it joins the ground track and battery track and you get power ... when you pull it out the battery ground floats and you save the battery and switch the device off.
Hope this isn't a granny egg sucking class or has been mentioned before, not read the whole thread and don't know how much of this you've done.
If you've not used Veroboard much then perhaps make something simple and useful for starters as a practice piece ... recommend the brilliant and simple buffer/pre. I get so much use out of mine for all kinds of stuff ... The Tillman (with or without gain switch or volume pot) http://tagboardeffects.blogspot.com/201 ... llman.html
(oops not sure if you have any JFets, but pretty much any will do)
My sincere apologies for posting the link to the Tagboardeffects site. I thought I'd managed to sneak it past you but Merlyn spotted it so you can blame him for all the hours you will likely now spend breathing in solder smoke hunched over a screen when you could have been outside, with a cold beer and Africa's finest between your fingers playing an acoustic guitar. Sorry.