As far as the stove top, you probably have two large burners and two small ones. If so, you can always divide your boil into two separate containers. Just a thought.
Minimalistic approach: use the pots you have, the stove you have, brew extract only, use buckets for fermentation, never measure gravity or fermentation temperature, bottle. Try boiling 4.5G in a pot on your electric stove and see how long it takes you. My stove (and my side-burner on the grill) took forever, so I got a dedicated propane burner after a few batches.
My first step would be going all-grain - so BIAB or dedicated mash tun. I think either one is fine, I still like a dedicated mashtun which also doubles as a regular large cooler for parties and trips and stuff. It also allows you to pour some hot water, throw the grains in, and walk away for an hour or three - or even mash overnight - the cooler insulation will keep temperature constant. Whereas BIAB will require some constant monitoring. Mashtun cost is under $100 including all parts.
I also think 5G batches are the way to go. I do 10G or even 15G batches now (just split them and add different additions or yeast) but to me 3G or 1G is a bit too far on "hours of work per amount of beer brewed" scale.
5G may be a sweet spot. The 5G fermenters are about the same price as 3G fermenters and can be found more commonly. I would go with 8G+ pot for 5G batches.
Then I would get a propane burner. It will really speed things alone, especially for 5G or larger batches. $50-60 would get you a nice one.
How are you chilling your wort? Large batches may require immersion chiller or something fancier. I like immersion chiller option because it's effective and easy to clean. But it takes some space and will cost you $100-120 for 25ft one, or you can easily make your own out of copper tubing (better one - 50 ft for about $50). Copper is getting expensive though.
After that, I would invest in fermentation temperature control. The simplest and most effective solution is a small freezer with temperature controller. That's maybe $120-$150. But it also requires space. You can do swamp cooler/ice bath to some extent as even cheaper way that is more limited and requires some attention.
The next step is probably yeast health. Make yeast starter and start your own yeast bank.
The step after that is replacing bottling with kegging. If you want to serve many beers at once, it can add up. Another freezer with temp-control, CO2 tank, regulators, manifolds, gas lines, beer lines, kegs, faucets, Nitrogen tank, disconnects, beer gun - it adds up. I think about 75% of my beer making "investment" is spent on the cold side of brewing (some fermentation, but mostly serving). Small items but they add up quickly - in my case about $2K in kegging equipment - but it is still worth it as I can scale up to bigger batches and brew more often.
Also, I would definitely invest in a hydrometer or a refractometer. It's like $20, but it prevents you from making a lot of mistakes and gives you some indication of what's going on with a beer. I really don't understand people (some are my best friends) who don't ever measure gravity - or temperature. It's a no-brainer. You also need a decent thermometer but you may already have one for cooking.
So typical progression in my opinion:
upgrade to 5G batches -> immersion chiller -> All Grain -> propane burner -> yeast health -> fermentation temperature -> kegging.
After that you have a lot of fancy stuff that doesn't make as much difference in my opinion (diminishing returns) - but it does look and feel nice. Like stainless steel conical fermentors, automatic brewing, electric brewing, etc. Cost escalate but they only save a small amount of time and make very little difference on the quality. You can make a great beer with $100 of equipment and you can make a terrible one with $10,000 of equipment.
