I've been trimming, then advanced to shaving, since before it was "fashionable", so I've tried just about everything out there to find what's best, for me, anyway.

Over all these years, the best thing I've discovered for the most comfy and longest lasting results is the newest razor they have on the market at present, the Fusion razor by Gilette. It's a razor that vibrates when you turn it on, (has a built-in battery safe in water use). The blades are SO incredible sharp that it provides THE best results, so long as you change them when they dull. The only drag about them is their price, but you do get what you pay for and for me the results I receive is well worth the price. The shave lasts me almost a week before I have to shave again

I always shave soon after the stubble begins to poke through, so the task of shaving isn't difficult. I shave completely clean. Of course, growth of hair depends on the individual.

If the razor is too costly for you, which I'd perfectly understand, and since you are new to shaving, the next best thing I would suggest to try would be any disposable "woman's" designed razor. I can't recall the name of them, but any razor that is disposable, or with disposable blades, again, depending on the price. I've found that Schick or Gillette is two of the top brands, and would recommend those for best results. If you chose to use a generic brand, pay close attention to the "life" of the blades, as the generic usually dull much faster. Also choose a blade which offers the extra moisturizer strips on the heads, (they not only provide easier shaving, but are a general indicator for expiration of blade..Once color changes, indicates when to change). Women's razors offer the extra moisturizers on the razor heads.

I've also discovered that at first shaving, and depending on how you choose to shave, (as like mentioned in other replies), trim pubes with scissors first. I bought a special "tiny" pair of scissors, which provides a much more accurate control of use. Fair warning though, use caution when trimming .It's not pleasant when snipping off a bit of skin in the process of trimming, (though, I used to get too close with scissors...that was before I began using blades to the entire buff).

When starting to use blades, ALWAYS FIRST shave in the direction of hair growth , (to remove), THEN against growth, (for the final shave). You can tell the direction of growth by running your fingers against skin after initial cut. If you feel stubble, then gently shave against the growth for that "baby butt soft" result.
Also, keep the blades rinsed continually as you shave. Hair buildup between the blades interfere with best results of blade's job.
NEVER "over apply" pressure to the razor. Allow the razor to do the work. After some practice, you will naturally be able to tell when it's time to change blades, (dull blades proves that shaving becomes more difficult and it leaves you with razor burn. If it takes more than a few stokes to shave a specific area, then usually that indicates time for new blades). Also, NEVER dry shave. You'll SO regret it.

I use the soap lather to condition as I shave, but you may find better results using the various conditioned shaving creams which can be purchased. Everyone's needs are different.
It's a general rule to shave in shower, or bath, as the hot water softens the skin around the hair which provides easier shaving, (and easier cleaning). If you choose to shave outside of shower or bath, you must first apply a compress of a warmed washcloth under water. Allow to remain on area for a few minutes to soften the hair area.

And after your shave, always apply a moisturizer to the area to prevent possible razor rash, (which may result depending on the quality &/or use of blade).

The best I can suggest regarding the prevention of ingrown's and discomfort of regrowth is the quality of blades used, use fresh, sharp blades, and soak in warm bath water prior to shaving. The softer your skin area before shaving, the better. And always use a moisturizer afterwards.
It's a combination of shaving tactics used that assists in the best results afterwards. Trial and error, experience and, of course, skin sensitivity ALL plays a crucial role in individual results.

Oh...One more thing...I have discovered that shaving buff, then armpits ALWAYS take precedence before the legs. For me, the legs seem to have always dulled the blade long before they should be. So, I've eventually purchased two razors; One for legs ONLY. Nothing worse than to drag a dull blade on the buff.....OUCH!

That's about it. Good luck. Happy shaving.

Shangrala