When I started I did a bunch of 3 gallon batches for the same reasons you mention. Now I have transitioned into 5 gallon batches and 2 gallon batches.
I tried 1 gallon batches but its far to little beer, and way too hard to control the final amount of liquid obtained, as well as measure everything in such small amounts. I also enjoy tasting the beer after 3 days, 1 week, 2 weeks, etc. And see how it ages and changes. There is not enough beer in a 1 gallon batch to really do this to much. These are the reasons I moved to 2 gallon batches.
I would recommend doing 2 gallons at a time for the reasons I mentioned above.
Heres what I would recommend equipment wise and why.
Buy an 8 gallon stainless brew pot. This will allow you to do an occasional 5 gallon batch should you like a recipe, as well as when you are ready to move up you will already have it, it still works great for 2 gallons (not for 1 though, its too wide). This will be the most expensive thing you have to get.
Buy the biggest, strongest BIAB bag you can find. I like the ones from austin homebrew but there are many others. 1 large bag is enough for 15lbs of grain so again it will work for your 2 gallon batch or a 5 gallon batch.
Get a small ice chest. This is where I modified my BIAB routine. I still keep the grains in the bag but I mash inside a small ice chest because it keeps the heat for a full hour. The taller ones work best for small batches, and its nice to have the whole to drain out of into your pot. You probably already have this.
You will need something to ferment in. The best way to get 1 gallon glass jars is buying sangria at your local grocery store. I can usually get a gallon of it in a glass jar for $9. A 1 gallon empty from the brew store is $6. You will want 2-3 of them. (The third is just in case you overshoot your quantity a little, or want to ferment multiple batches)
you will also want an auto siphon, funnel, stir stick, 3 piece air locks and stoppers (6.5 size fits those 1 gallon jugs, if I remember right). Then 1 or 2 liter/20 oz soda bottles make great cheap bottling items. All of these items are needed for any size batch.
It sounds like a bit of equipment but you may already have some, and it should be fairly inexpensive to get them all.
Some other tips for such small batches.
Boil 3 gallons of water in your pot for an hour on the same stove you are going to use. How much water did you lose? I need to start with 3 gallons to end up with something like 1.8 gallons after mashing and boiling.
Do you have a scale to measure your hops? At such small amounts slight mis measures make a larger difference.
1 gallon batches is VERY hard to get the same amount of water at the end of boil. How vigorous you boiled makes a much bigger difference is such a small amount of wort. This is the biggest reason why I moved up to 2 gallons.