Very often, we may take elixirs without supplementary ones. The question you have to ask yourself is 'Am I concerned about maxing that lvl of elixir? Or will I simply be satisfied even if it is not maxed?'
Retaking elixirs of the same level is costly. If you take a 1st elixir without a supplement hoping to max it, but it doesn't, and you take a 2nd one, it is as if you had not taken the 1st elixir. It is as if you threw some money away. Supplementary elixirs, the mushrooms in particular, increase your chances of maxing. You should weigh the costs and benefits before taking elixirs without supplements.

General elixir consumption tips

Consume your elixirs in a safe area. Getting attacked while consuming an elixir always results in failure, with a negative stat 'bonus' resulting.

Consume an elixir only when your intoxication level is 0. Higher intoxication levels decrease the chances of maxing and increase the chances of failure.

Ensure that you have no external and internal wounds when consuming elixirs. Wounds tend to result in lower stat boosts (from my experience).

Consume dungeon elixirs, sell or use non-dungeon ones for WD weapons. The prices between dungeon and non-dungeon elixirs makes it worthwhile for you to sell the non-dungeon one and buy a dungeon one, and you can make some money in between.

How do I use supplements?

Supplements are consumed before taking an elixir, and will only work for the 1st elixir you take after consuming the supplement.

Can I use more than 1 supplement?

Unless future patches introduce any changes, supplements cannot be combined for greater effect. Only 1 supplement may be consumed per elixir you intend to take.

Recommendations

Lvl1s and 2s may be taken freely. They're prices are low and you can collect them easily from CoF and VoH.

You should consider consuming blood mushrooms with lvl 3s and 5s, or blue stone mushrooms with 5s and 6s; 4s may be taken with BMs as well. Do also give consideration to the relative prices of elixirs and supplements in deciding what to take. It is more pressing to consume a BM with a lvl 3 than it is with a lvl 4 for example. As the prices of BSMs fall relative to elixirs, you can consider consuming them for lower level elixirs.

If you are more concerned about avoiding failure, which brings with it negative stats, than maxing a particular lvl of elixir, lotus leaves and purple bamboo shoots are your answer. High level elixirs, especially 5s and 6s, are known to adversely affect unlucky people with a fairly significant probability, bringing with them negative stats up to -9. Generally, take lotus leaves with lvl5s, and bamboo shoots with lvl6s.

Dilemma

BMs and BSMs do not lower chances of failure. It is possible and very expensive to fail when taking mushrooms with elixirs.

Lotus leaves and bamboo shoots do not increase your chances of maxing. Consuming them with your elixir simply adds to the cost if you fail to max it, and is a waste of money if it would have succeeded anyway (then again, we cannot tell what would have happened otherwise).

Retaking Elixirs

"Damn... It failed to max..."

There is no need to max a lower level of elixir before moving on to higher level ones. You can retake lower lvls freely after consuming higher lvl ones, without compromising your chances of maxing them.

"Should I retake that lvl I failed to max? Or should I leave it and move on to a higher lvl elixir?"

Weigh the costs and potential gains between retaking that elixir and moving on to the next lvl. If you can gain more stat points at a lower cost, go for it. For example, if you fail to max a lvl3, consider leaving it till later. With that same amount of money, you could consume 1 each of lvl4 and lvl5 dungeon elixirs, which is a potential 11 point gain compared to the few points you could by retaking the lvl3. Do remember your mushrooms though.

Summary & Conclusion

The final and long term goal is to max your elixirs, and the cheapest and quickest route there is to consume the appropriate lvl of elixir with the appropriate type of mushroom. Do not let the occasional ill fortune discourage you.

In short, if your goal is to max your elixirs, max them with the lowest expected cost.
A secondary consideration is to gain as many points with a given amount of money (when you fail to max).