There is much conflicting information regarding the amount of toxic mercury in various fish. But, there is agreement that the benefits of eating fish far outweigh the dangers of mercury. 
Fish are among the healthiest foods that humans can eat. They provide an excellent source of protein, important nutrients, and healthy fats for the brain, the nervous system, and heart.
So, what is the ideal amount to consume? The FDA recommends that adults may safely eat up to 12 ounces of fish per week, as long as they avoid the large predatory fish.  The smaller the fish, the less mercury it stores.
The 12 ounce limit amounts to about two meals per week. Healthline  lists the amount of mercury found in various fish species.
Shrimp, scallops, sardines, oysters, and anchovies have only trace amounts of mercury.
Salmon, catfish, and canned light tuna (not albacore) have slightly more of this toxin.
Haddock, crab, trout, whitefish, lobster, cod, and canned albacore tuna contain medium amounts of mercury.
According to the National Resources Defense Council (NRDC) , it is best to avoid the following fish, due to their large content of toxic mercury:
- Ahi tuna,
- King Mackerel
- orange roughy
The American Pregnancy Association  has a handy list of fish that can be consumed two times per week:
Trout (fresh water)
It is recommended to avoid eating the following fish more than 3 times per month:
Chilean Sea Bass
canned white albacore tuna
Besides mercury content, the decision regarding consumption of farmed vs. wild-caught fish needs to be considered.
Wild-caught fish are strongly recommended over farmed fish by Dr. David Perlmutter, author of Grain Brain. Farmed fish are contaminated with 16 times more cancer-causing PCBs than wild-caught. Farmed fish are pumped with antibiotics, and they contain a much greater proportion of inflammatory omega-6 oils. 
Unfortunately fresh wild-caught salmon is not available all year. It is generally available late spring through early fall.
Generally, if the fish is labeled Atlantic, it is farmed. If it is labeled Alaskan, it is wild-caught. Otherwise, if not expressly stated as wild-caught, assume it is farmed.
One final note regards tilapia. It is one of the most popular fish consumed in America. Ironically, it is one the most important fish to avoid. Farmed tilapia is the only type available in America. This fish is highly toxic, inflammatory, and can lead to serious health concerns. Many sites advise against its consumption.
Joe and I rarely eat farmed fish. Our one exception is salmon. But, we always select wild-caught salmon when it is available at the grocery store or a restaurant.