I don't have any recipe advice for battered fish. I dredge all my fish at home in a 95/5 ratio of corn meal to flour with seasoning, typically old bay. Simple is good here. I like the light crunchy coating and the simplicity of a dry dredge. Sometimes I will use an egg and milk mix to help the coating adhere to the fish. After a long day of fishing, driving, and cleaning you appreciate not making a batter. Consequently I have never found a battered fish recipe I truly loved and would share. Alton Brown's recipe is good but be sure to choose a real ale for beer battering the fish! The only fish I fry at work is catfish and I just haven't ever seen it heavily battered in the British fish and chips style.
My recommendation for deep frying at home is to use a large cast iron pan, dutch oven, or any suitable heavy pot. I never use a proper deep fryer at home and it's always done over a gas stove. There are submersable fry thermometers available in most stores that clip to the edge of a pan but I think they are clumsy and dangerous. My electric probe thermometer works great for deep frying, I just swirl it around in the oil until it reaches the desired temperature (~365F is a good starting point for a handful of small fillets). The fish will cool the 365F oil upon contact and fry somewhere in the 350F range. If the temp drops far below 350F then you need to increase the oil, add less fish, or increase your starting temperature. The proper combination of these factors is paramount. Don't forget to let your oil rest and recover temperature between batches. This makes the difference between crispy fish and grease laden fish. The heavy pan is necessary to retain heat but you can mitigate this factor with a greater amounts of oil. I would rather spend a few more minutes frying than keep gallons of oil laying around the kitchen. My 6 qt dutch oven is most commonly used with around 5" of oil in the bottom. I keep the oven at it's lowest setting for keeping fry batches warm on a sheet tray. This amount of oil only comes about halfway up the pot but prevents a lot of the oil mist and spatter that gets out of control with a huge vat of oil. Do NOT cover the pot while frying as the escaping moisture from the fish will condense on the lid and drip back down causing all kinds of disasters.
I only use canola oil at home for frying. It is flavor neutral, inexpensive, has a high smoke point, and is stable enough to last a few meals before I want to strain it and reconstitute with fresh oil. I always reuse a portion of old oil when when adding fresh. I've had a lot of cooks tell me this is necessary to maintain a certain flavor and texture profile. Personally, I think it mostly maintains a profit margin but I have no complaints. Peanut oil tastes great but the price is ridiculous and I don't trust vegetable oil blends. Pure shortening works pretty well if you feel like experimenting sometime (amazing with fried chicken!) Temperature control is the key to getting long life out of your oil. It can last a long time at 350-375 but get it much over 400 and it will start to break down into stinky mess. Honestly, I don't change mine until it starts to look like used motor oil. Not neglected motor oil, just well used motor oil. When it starts to taste like corn chips at a bad mexican restaurant it's time to change. It will develop a bad rancid flavor (along with a few carbon compounds you don't want to eat) but once again, keeping an eye on those temps will do wonders for oil life. I pour my used oil over a simple strainer to collect the flotsam and chunks leaving the fine corn gritty "slime" behind, and pour it straight back into a bottle when cooled. Or just put it back on the stove with a lid on it like I do during fish season. It stinks like Long John Silvers but I cook for a living and consider it one of the charms of wearing an apron all week and frying fish at home. Your hushpuppies will taste better in the fishy grease too.
Hellman's and kraft actually make a decent tartar sauce IMO. It's dead simple to make but it complicates those simple 1-2 person fish fry dinners and I don't make it from scratch unless we have company over. Mayo, pickle relish, fresh lemon juice, perhaps a dash of Worcestershire sauce..... that'll do it. It's the pickle relish and lemon juice that make the difference. Just mix to taste. Malt vinegar is an even easier alternative and more in style with heavily battered fish.
Sorry.... I don't have much to help with your chips. They are a true PITA to do properly at home. Usually it requires cutting the potatoes and allowing them to soak in water overnight (to begin the starch to sugar conversion) and then double frying at two separate temperatures. I love 'em but I stick to hushpuppies, southern style green beans, or fried potatoes when I'm at home.