I have been thinking about getting into reloading.
Don't even think about it unless you have time to spare, are somewhat mechanically inclined, and are patient.
I don't shoot that often but I like to have ammo on hand for when I do. I have about 400 rounds of .38 130 grain target ammo, plus about 200 rounds of my old duty ammo, but I don;t want to shoot that stuff at paper. IF you can find it at all, winchester white box .38 target ammo is $20 a box. That is just insanity.
Yes, insanity. And it isn't going to get better. As prices increase, saving 40% of $100 worth of ammo will become saving 40% of $200. You can make 9mm for about what you might pay for 22LR now, if you can get it.
I have been saving my brass for the last 2 years and probably have 400 spent cases.
Keep doing this, and pick up others' brass as well. I know I can get the press, and primers are becoming a bit easier to find, but powder or bullets are nowhere!
Bullets are available - for pistol check Berry's Bullets for example. Powder comes available, and you have to jump on it immediately when it does. You need to keep a 6 month supply minimum atm to stay supplied - it could take that long to get replacement stuff. And get used to ordering by the thousands 
I'm not gonna start casting lead bullets.
Me neither 
I am literally looking to load 300 rounds or so at a time.
That's a nice upper limit for a Lee Turret Press. A progressive will take longer to do a caliber changeover than it would to make that much ammo. I doubt I shoot more than 500 rounds a year through my .38.
First of all, what is REALLY needed? I can get a Lee Turret press for around $225 that comes with most of the equipment.
Start with the kit. Use it and add/replace stuff when you actually experience the need to. But I figure I need a tumbler to clean the brass, and a digital scale
The Lee scale is a PITA, but it works. Cheap digital scales are next to worthless. Get a set of RCBS check weights instead of a second scale. You will then have confidence that your scale is set extremely close to your target weight(s). You also need a way to separate tumbled brass from the media - a covered media separator keeps dust in - OTOH a colander works too. Lizard Bedding from Petco (eg) is crushed walnut and works well. , plus the literature, etc. I'm thinking all in start up costs would eb around $500 if I could get the powder and bullets.
Yup, $500 now and probably another $100-$500 as/if you progress to higher volumes and/or better equipment. You could watch for powder, then when it comes available pull the trigger on everything else.
I have beens aving my 9MM brass and recently got a Garand so I save that too, so it wouldn't just be for the .38.