I sympathize since I too had to cover the cost of my dental work out of pocket, but it was worth every Yen.
The chelating method you choose really depends on you. Some methods seem to work better for some while not working so well or causing a major reaction for others.
Some popular methods include:
The Cutler Protocol: Many people swear by this one. It uses DMSA and ALA while some people use ALA by itself. You should wait until 3 months after you replace your fillings to begin using ALA.
Cilantro and Chlorella: This method led to the most obvious improvement for me, but there are people who worry about whether or not this method is safe. I haven't had any trouble (except for the fact that I have worse temporary side effects while using it, but they go away after I finish a round). My friend has used it too with no trouble.
DMPS: I haven't used this one either injected or orally, so I can't comment on it.
There are other methods as well, but I haven't tried them.
The key point with chelating is that you do it frequent dose every 3-4 hours, including at least once during the night to keep the effect going and prevent redistribution. As you improve then it's helpful to increase the frequency to every hour or every 2 hours. It's also important to take breaks to let your body replenish chemicals which help in the chelation process.
Vitamins to help with this process include: Selenium, zinc, vitamins C and E. There are others, but it may depend on who you listen to and believe.
Eating foods which help glutathione-production, drinking lots of water and taking sauna baths are very helpful too.
The most important thing about chelating is to remember that improper chelating can be dangerous, so make sure you do a lot of research about a particular method before you begin using it. You will likely need to modify the methods somewhat to fit your body and situation, but it's not a good idea to change them too much. That can be very risky.