Is it better to save for expensive items or buy/sell cheaper items?

Needlessly Large Rod is the second most expensive item in the basic tier (1600 gold), the most expensive being B.F. Sword at 1650 gold.

When I need to purchase those items for recipes, I feel really inefficient waiting to farm up 1600/1650 gold to get them.

I was thinking about purchasing Doran items. However, they sell for 50% of their purchase price, so it might create a bigger problem.

So, my idea is to buy 400g~800g items, and then sell them for the 1600 gold to purchase the B.F. Sword and/or Needlessly Large Rod. The time spent farming that gold can be spent with the better stats of the intermediate items.

Which intermediate items would you recommend for this? Or is there a better reason to wait til I farm the 1600/1650 gold to buy them directly?

When to buy those items is very situational:
Assuming generic AD carrys like Graves, Sivir, Miss Fortune or Ashe, the first time you go back to base you should buy 1-2 Dorans Blades and a few Healing Potions instead. Those items help you stay in lane longer with their health, lifesteal and damage bonus, which allows you to farm more gold before going back the next time. They are what empowers you to actually get that B.F. Sword.
Don't buy Berzerker Greaves first because they don't actually help at all. You won't be attacking constantly but in bursts instead, so the Dorans Blade that you should buy instead actually has a bigger effect on trades.

If you can stay in lane long enough because the opponent doesn't harass or is completely outclassed, you can get the B.F. Sword immediately, but that rarely happens in a normal game. You need the small edge that Dorans Blades give. If you come back to lane without a Dorans Blade and your opponent has two of them, he can completely bully you around and free farm on a frozen lane while you sit under tower, not getting any farm or experience.

Also, if you can't afford the biggest component, for example for the Infinity Edge, you can get a smaller component like the Pickaxe first (after Dorans Blades), which still builds into the same item and makes you stronger in lane than if you would wait for the big item.

"Selling items is bad" is mostly true, but:

• If the item you are buying now is helping you to stay in lane longer (i.e. Dorans Blade/Dorans Ring) then it is worth it because by staying in lane longer, you gain more gold than you lose from selling it.
• If you come back to base lacking 200 Gold for your next major item (Infinity Edge, Bloodthirster, Phantom Dancer), going back into the fight without it would make you weaker now and potentially put you further behind than selling one of the Dorans Blades and getting the big item now.

It's all about short term benefits giving you an edge to have a bigger advantage later.

All of this is true in the same way for AP carrys with Dorans Rings.

Never try to purchase stopgap items just so you can sell them later for your build - that just means you end up wasting a lot of gold and makes it even harder for you to get anywhere near your full build.

Doran's items are actually among the most efficient in terms of stats for gold spent, which is the reason people often use them for a good start. The idea behind this is to use their stat boosts to help in the laning phase, so that you can get the CS to afford your build.

Alternate Item Purchases

What 400-800g items are you planning to buy in lieu of BF Sword or Needlessly Large Rod, that are useful for a hero but not part of his build? Usually, these are components in a recipe, so if you want to get some item then you should look at the other parts instead.

For AP casters, maybe go for the 860g Blasting Wand first en route to completing your Rabadon's Deathcap. For AD, its often useful to pick up an early Vampiric Scepter for sustain, and it doesn't hinder any plans for an early The Bloodthirster. If you're directly aiming for Infinity Edge, the sustain will hopefully allow you to remain in lane a bit longer and pay for itself with more CS gain. Another option if you're doing really well in lane, is to invest in GP10 items esp. those that are part of your build - ie., Kage's Lucky Pick when you plan to pick up Deathfire Grasp, Avarice Blade for AD crit builds, Heart of Gold for tanks, and Philosopher's Stone for anyone.

Why/when to farm the 1600/1650 gold to buy them directly

These 'expensive' items are actually the most cost effective for their stats - a single 1600g rod is more powerful than two 860g blasting wands, and only occupies 1 slot in inventory. So if you're doing well or at least even vs lane opponent, backing only after you save up the full amount (+ some extra for wards) is a chance to get dominance over your lane opponent for some time (e.g. when you have BF sword and he only has a Doran's & vampiric scepter)

Selling items is a bad idea in general. You need to remember that items only sell for 70% of their price:

1600 / 0.7 = ~2285 gold
1650 / 0.7 = ~2357 gold

That means you need to farm 600 gold or more if you temporarily buy items. You could spend this on something else (e.g. upgrade your boots).
For Dorans and gold generating items the buy/sell ratio is even lower with only 50% return.

Most of the time, the best thing to do is to stay in lane and last hit as much as possible. This lets you not only gain gold more consistently but also ensures you do not miss Experience compared to your laning opponent.

From my (quite limited) game knowledge and experience, an AD carry wants to stay in the lane until he has farmed enough gold to buy a BF Sword and maybe boots - unless he needs some sustain or goes for Dorans Blade to put on more pressure during mid-game.

Even so, there may be some situations when you can not afford to wait this long to return to the base, e.g. when you are harassed too much and need some earlier items to be able to come back.