The older Singer ones (not the tailor one) should be easy to clean up, oil and grease and maybe see if they run okay. I don't know much about the tailor one and it looks more like it's a newer one that would be more difficult to do maintenance on like my newer machines. I have my Mom's old 403A (takes the black cams) and I got it in good running condition after my sister was going to throw it in the garbage when they moved. She didn't like the way it sewed anymore--just needed a good maintenance with oil and grease and a tension adjustment (both bobbin and upper tensions). It hums now! It's one of my back-ups. Good luck in getting these up and running as they don't make the new ones as nice as the old ones and as easy to maintain.
Also, if you don't have a manual for the 503 I have the book on it (503 Special is the title) that the sewing machine shop gave my Dad when he bought the used 403A. I have since gotten a copy of the 403A instruction book on Ebay. If you PM me with your address I can send it to you. I also have 4 extra cams that it would take: #3 diamonds, #6 crescent, #7 icicle, and #11 ribbon you can have also.