Be aware, once you start reloading you'll have a period of at least 2 or 3 YEARS where you will have some doodad on your want list to make it easier or faster. The end result is that 300-400 dollars can get you a good basic setup but once you get really involved and start adding calibers you'll find your total outlay to be well north of a Grand. Now the positive to all this money spent is that you won't ever have to wait for a shipment to arrive at Walmart, you'll just assemble your ammo as you need it.
Basics. A good place to start is with a Single Stage Press. While it's not particularly fast it is a very safe way to reload, presses are fairly low in cost, and you'll get a good grounding in the basics of each operation. BTW, I shoot between 700-1500 rounds per month and have no problems keeping up with my usage using a single stage press.
Brands. IMO the best buy for the money for equipment is RCBS. I'll also point out that I've reached this conclusion after trying less costly products from Lee and Hornady. My Press is an RCBS Rockcrusher Supreme (119.00 on sale, 145-160 not on sale). Powder Measure is an RCBS Competition Rifle/Handgun set (about 170 bucks - ouch) and was chosen after having had enough with the Leaky Lee powder measures. For ease of use, ease of setup, and repeatability of throws and setups that expensive RCBS is worth every penny. Scale is the RCBS 502 (70 bucks on sale - 80 bucks the rest of the time) and like most scales it has it's hidden pitfalls but used properly it's accurate and the zero doesn't change as long as you don't knock off you bench. BTW, the hidden pitfall is that the heavy poise sometimes doesn't fully center itself in the chosen notch, so tap it in lightly with a wood pencil or powder dipper to vibrate it in. Also have a Frankfort Arsenal Digital Scale (30 bucks) and it is accurate when first switched on but the zero drifts after a couple of minutes, so it's used to confirm my beam scale is set correctly.
Case cleaning. This is something that really doesn't need to be done. Vibrating tumblers sort of work OK if you aren't real picky but deep revolver cases will not come out perfectly clean no matter how long you run them. If you go really cheap you can get a Harbor Freight tumbler for about 65 bucks and wear it out cleaning about 8000-10000 cases. If you feel like spending more Lyman makes a tumbler with a reputation for lasting for many years of use. Ultrasonic cleaners tend to rely on a cleaning solution that is a bit acidic and that will leach the zinc out of your brass so that will shorten the life of your brass. If you want brass that looks sparkling new the only answer I've found is the Thumlers Tumbler with stainless steel pins, a 250 dollar investment that will likely last for 30 or 40 years.
Brass. Best brass for the money is Starline and if you order direct it's a real bargain. However there is a "trick" to ordering any of the more popular calibers. If you go on the Starline web site you will find that a lot of calibers are listed as Not in Stock - No Backorders. At some point you'll see that Backorder status change from No Backorders to Backorders Accepted. When you see that happen you don't think about it or wait to make up your mind, you place a backorder for the brass you want. Within a month you'll see a notice that your brass has been shipped and you'll find the charges have been submitted to your credit card. What happens with Starline is that when they schedule a production ron for a specific caliber they will open up the Backorder list until the total volume for that run has been pre-sold. On rare occasions when the backorders don't fill out the scheduled run any extra brass will then go into inventory and be listed as Available. However, that doesn't happen often and its only with the less popular calibers so if you want new brass wait for the Backorder list to open. BTW, Starline ONLY charges you when your order has shipped, so they don't charge ahead of time and use your money for some short term investing.
Primers. Primers have finally become widely available, however the cost per thousand has increased by 5-10 dollars at most vendors. I personally wait until they go on sale at one of the local vendors and purchase a box of 5000. If you can't wait for a sale plan on spending about 39.95 per 1000 because that is the most typical price I've been seeing.
Powder. That is currently a problem with Handgun suitable powders because they just don't seem to being produced in any volume. Some good news is that the 44 Magnum can use H110 can be located with some looking. For your 44 Special loads it's going to be a lot more difficult to locate a suitable powder. BTW, IMR SR7625 is a real favorite of mine for semi auto loads in 9mm, 40 S&W, and 45 ACP but I can only recommend strongly AGAINST it's use in any revolver load. I tried it once in 38 special and found it so position sensitive that there was a 300 fps difference in velocity depending on whether the barrel was pointing up or down prior to a shot being fired. Powders suitable for a 44 special using a jacketed or plated bullet are likely Accurate #5 or #7, Unique, Vihtavouri N330 or N340. For soft shooting Cowboy loads featuring lead bullets I expect that Trail Boss will prove a great choice.
Bullets. I like plated bullets as does the indoor range I shoot at most often. Note, you'll find a lot of indoor ranges are now banning any load featuring lead bullets because the smoke produced by the lube tends to clog up their very expensive HEPA filters too quickly. As for brands, I've found that Berry's, Rainier, RMR, HSM, and Extreme all make excellent bullets with plating suitable for velocities up to 1200 fps. Some of these brands also offer Heavy Plate bullets in selected weights and types and a slightly higher cost that are rated for velocities up to 1500 fps. Recently Extreme has had the best prices so that is where most of my bullets come from but they don't offer an Heavy Plate bullets in the 38 caliber at this point so my 357 Magnum bullets are Hornady XTP's.
PS; It has been about a full 18 month process of going to every local gun show and treking to a couple of shops in Ohio but after this mornings trip I am finally in the position of not needing to purchase any primers or powders for at least 3 years. Hopefully by then this component drought will have ended and I won't have to go through all the effort this past year has required. Point is, even as hard as it is right now to find handgun powders it can be done if you put in the effort.
