How to effectively engage enemies at medium to long range?

It's my experience that shooting at long range is ineffective even when you have quite high firearms related skills.

As you say, the solution therefore is to close range. There are several tactics for doing this, including increasing your Stealth skill and crouching to approach (i.e. sneaking up on the enemies), Stealth Boys (expensive but effective), and use of terrain to remain in cover while advancing.

The "Gunslinger" (1 handed) and "Commando" (2 handed) perks will improve your VATS accuracy. "Sniper" (at level 12) will improve your accuracy with VATS headshots. These will push up your chances of hitting at long range.

Wired reflexes (quest perk, can get perk and weapon), sniper, gunslinger, commando, concentrated fire are the accuracy related perks.

The easiest method though is to just save before long shots or use zero spread weapons like lincoln's repeater.

My favorite for medium to long range is the Gauss Rifle. It's a reward from Operation: Anchorage, which should be done towards the beginning of the game because you also the Power Armor perk, virtually unbreakable Power Armor, Chinese Stealth Armor, and the most powerful sword in the game.

The sniper rifle is the best rifle in terms of sniping. When you go into tenpennys suite and you see him sniping, kill him and take the rifle.At long distances, bullet spread at 0 still wont hit head on. You have to consider bullet drop. At longer ranges gravity will act on the bullet more than shorter ranges and to compensate for this aim higher up than your target. The accuracy determines on the skill of the player not the gun or perks he carries. With a sniper you can hit as far as you can see. You just need to know how.

Unlike some answers above stated, there is no bullet drop in fallout 3, or New Vegas. However the game does have issues with scopes being misaligned, which means at longer ranges, the centre of the scope may not be where the reticule is actually pointing

The Big Guns, and Small Guns skills, do actually affect both Accuracy (Spread), and Damage for guns effected by them. Energy weapons skill only increases Damage.

If you want a exhaustive list of all weapons, and there stats, including spread, click this link

Crouching also reduces spread, as does aiming down sight with the weapon. See this for more info.

The "accuracy related perks", only affect weapon accuracy in vats, and are multiplicative based on the number they state.

VATS should be avoided for long range combat, as distance reduces accuracy,meaning at any meaningful distance, your accuracy, even with VATS accuracy perks, will likely be very low. However, with certain guns, such as the alien atomizer (which has a very low vats shot cost) from Mothership Zeta, certain builds allow 10+ shots in vats with it, which with combined with the Concentrate fire perk, can raise your chance to hit by over 50%! Of note is the fact that the alien atomizer also has 0 spread outside of vats also.

The best advice I can give you, is to get a Sniper Rifle, or a Hunting Rifle (The Unique Ol' Painless is easy to acquire hunting rifle wise, boasting no spread!!!).

The reticule of any scoped weapon is going to be off at long distances. So if you are using the Sniper rifle for instance and you have a target, let's say 200m away, then I recommend you put the crossing point of your sniper optic at his feet. So exactly where the crosshair crosses, put it at his or her or its feet (or lowest point) to hit them center mass or even dead in their face. You will see what I am talking about when you try it out. It's pretty satisfying when you get the hang of it. Long story short, sniping with modded scoped weapons or just the sniper rifles (common and legendary) at long distances, aim for their feet to hit them center mass or higher!!!!