So would it be better to use bags of shock right now until levels go up and then move to TFP?
That all depends on a lot of factors. Do a full round of tests including your calcium hardness (CH). I wouldn't be too concerned about your PH or Total Alkalinity as long as you don't run them off the charts one way or another (meaning no reason to try to LOCK IN 7.6 PH or 80-100 TA until you get everything else settled), which you shouldn't as long as you are only adding some variety of chlorine and CYA.
The reason I ask about CH is because if it is low, then yes, adding a powder shock such as Calcium Hypochlorite (Cal-Hypo) will help raise that while also chlorinating--i.e. saving purchasing another product, killing two birds with one stone. But if your CH is high or in range, you don't want to use Cal-Hypo.
To your question, I think using bleach/liquid chlorine now is fine, but the reason I might go a powder route temporarily is if you need to get your CH up, which you probably do a bit, even as our water in the metroplex is considered on the hard side. My CH out of the tap for fill water usually registers about 150ppm, give or take. I would imagine yours is similar. I usually try to get my CH to 300 at the beginning of the summer so I can mostly forget about it the rest of the season. Since you just did a full fill, I bet your CH will be between 100 and 150, so each pound of 73% cal-hypo you add for chlorinating will up that number by approximately 2ppm on your pool size.
Don't buy it by the bag, it is way more expensive. As much as I hate having to do Leslie's, for Cal-Hypo shock, their Power Powder 73% stuff is the best. The other stores are usually less potent or have some additives (what is up with the Clorox brand adding copper?). So using a 25 lb bucket of cal hypo for initial chlorinating will get you where you need to be and then you switch to liquid after that. Yes, you could go buy calcium chloride to make the increase all at once, but that is just something else to buy. One of the reasons to use liquid for chlorinating is the lack of additional added ingredients and cost. From a cost standpoint, going and buying calcium chloride to up your CH plus using liquid, will end up the same or more than just using cal-hypo at the beginning.
The same goes for my suggestion on using trichlor tabs right now until you get your CYA in range to protect your chlorine from the sun. Trichlor adds chlorine in slow release as well as CYA. Each 3" "puck" of trichlor, will kick in about 1ppm of CYA for your pool size. Since you want that to 50ish, you could use a few of those in the beginning to help with the CYA raise while also adding some slow chlorine so as not to have to make several chlorine dumps (powder or liquid) during the course of the day. The trichlor will help stave off algae and then you can do one total chlorine add right at sundown to maximize the efficiency of the chlorine (overnight with no sun loss). Since the best cost on tabs is around the 25lb mark ($60 at Home Depot), you will have 20 or so to use during this ramping up time and then the rest to use over the next couple of years for vacation stints or times you need to slightly raise your CYA again. I like the ones from Home Depot because they are individually wrapped and seem to still be quite potent even as I have used them up to two years later.
But I am no pro. I do what makes sense and it has worked for me. Others may have different or better suggestions.
One other thing, there is an on-going thread about best value for liquid chlorine/bleach and I regularly chime in with what I am finding in our area. You can find it here:
https://www.troublefreepool.com/threads/88742-Best-Places-to-Buy-Liquid-Chlorine
Right now, the best value is WinCo at $2.00 for 121 oz of 8.25% strength or Home Depot at $3.33 for 128 oz of 10% strength (3 pack/$9.99). Sometimes WinCo has it on sale for $1.75 or even $1.39, which is exceptionally awesome. I will say that I usually hit Home Depot for at least 4 three packs early in the season because they come in these nice heavy cardboard boxes that I keep in the back of my SUV so when I buy elsewhere, I do not have loose gallons to possibly tip over. I just drop them in the boxes and don't have to worry if I take a turn too sharp (FUN!) or have to lock up my brakes (idiot drivers!). Aldi and Walmart have fair deals also, so the best value may end up being who is closest or most convenient to you rather than the absolute rock bottom price. But be sure to check date codes and get fresh stuff--that is discussed also in the linked thread.
Everything you are doing so far is spot on...good job!
