I can say that most reviewers put the Earthwise 7 blade ahead of the Fiskars reel when it came to bermuda grass. I have one myself. More blades is better for lower grass, and it helps that it is cheaper too. It also has a roller on the back instead of just wheels so less likely to scalp. The other equipment you should spend the money on is a backpack sprayer. Trust me, no one has ever gone from a hand can to a backpack sprayer and then been like - well, that's not any better. It is night and day difference. I read a zillion reviews (I overthink things) and got the Rural King 4 gallon and love it more than my children some days. Such a difference. Oh, and get a spreader, but you can find those for cheap on facebook marketplace, craigslist, etc. I have a drop spreader I got for $15 that is normally $50. And it works way better than the new one I bought that was $40 - that one I returned.
And let me say, i hear you on the under achiever lawn thing, lol! That said, honestly, IF you can spring for some chemicals up front they aren't that expensive over time. PGR you can buy in smaller quantities in the marketplace here on this forum, and it REALLY does great things for the grass - not just less mowing but studies show it makes the grass healthier and more drought tolerant. I let mine come out of regulation and ever since I've been dealing with drought stress and fungus - I really regret missing that application! So I'd try to budget for a bottle of that - just a split from someone on the forum.
Weed control again you can get split bottles here - Celsius is worth it, especially in the heat. I did play fast and loose and go with Dismiss instead of Certainty, despite the heat, and did okay. I'd HIGHLY suggest getting some Quicksilver for that backyard - you can use it very early on after seeding/sprigging - sooner than other things - and weed pressure is no joke when seeding summer lawns. i tried to go without it and I am STILL regretting it months later. I have major bare spots I'm filling in now because they got taken over by weeds and crowded out the grass. By the time I finally sprayed and killed the darned weeds the bare spots were gigantic. Had I done it right away I could have avoided that. You can buy small amounts of quicksilver on amazon as it is pricey in the normal quantities.
Fertilizer is easy to go cheap on. Generic is fine. Do invest in a soil test (probably less than $20 at your state university or county extension office) so you know what the soil needs, then find something cheap and easy. I did spring for some XGRN 8-1-8 but may alternate that with a generic local 15-0-15 (I have high phosphorous already but need lots of potassium). The 15-0-15 is cheap and will work fine for my needs. Or when I seeded I again went with a cheap, all purpose 10-10-10 on greendoc's advice. Or if you want cheap per application but are okay with an up front cost you can get bags of urea or ammonium sulfate (depending on soil ph, etc) and potash and triple phosphate and mix your own custom fertilizer as needed. A 50 lb bag of 21-0-0 was $20 and will last me a long time, for instance. But as a newbie, if you are not looking to become a lawn geek mixing up stuff in the lawn and are not prone to way overthinking things like I am, just grab a bag of generic granular that fits what your soil test says you need. I will say the one brand name thing that is worth the price is FEature - it is a micronutrient supplement with chelated iron (only one that doesn't stain concrete)and that stuff will make your yard the greenest on the block and the micros will help balance out that generic bag of granular. Pick up a $10 or less paint mixer attachment for your drill and a 5 gallon bucket at the same time (for mixing it)
So my advice is, go cheap on the fertilizer, get the cheaper reel mower (earth wise), a mid range backpack sprayer, and then spend on the good herbicides, but look for smaller splits to get you going.
So needs:
Water
Fertilizer (cheap generic is fine and probably better than some pricey snake oil stuff *cough* super juice *cough*)
Mower
Backpack sprayer
edger/trimmer (I use a $30 manual rotary edge and a pair of long handled lawn shears but you can find gas ones on craigslist)
spreader
quicksilver for the seeded back yard (trust me - I can show you scary pictures of weeds in a seeded yard)
Celsius (split bottle)
Quinclorac (maybe?) split bottle or regular one - low annual limit so split is probably better idea if small yard
Herbicide for sedges - I use Dismiss because I have globe sedge, but there are other options including big box store depending on what you have
PreEmergent for front yard once it is rooted down, for backyard after filled in.Can get generic granular at big box store for cheap up front or look for a split of liquid on marketplace on this forum
Wants:
FEature
Kelp/Humic/etc