Data Selection according to Feature Values
Ignoring for a moment the variance of the first feature, a straightforward approach is to perform a linear combination of the features $x_1$, $x_2$ and $x_3$, with each of the coefficients being a hyper-parameter you set to indicate the relative importance of that feature (perhaps normalizing the features before hand). This will be your molecule's utility measure.
$$u^{(i)} = \beta_1 x_1^{(i)} + \beta_2 x_2^{(i)} + \beta_3 x_3^{(i)} $$
You can then sort according to this utility and select the top 1000. A natural set of coefficients if each feature was of comparable importance would be $\beta_1=1$, $\beta_2=1$ and $\beta_3=-1$ (negative because we want to select for low values of heuristic value 2).
Knowing that we have the variance of the first feature, we can assume that this feature is distributed normally. The utility is now a random variable distributed according to:
$$U^{(i)} \sim \mathcal{N}(\beta_1 \mu_{x_1^{(i)}} + \beta_2 x_2^{(i)} + \beta_3 x_3^{(i)}, \beta_1^2\sigma_{x_1^{(i)}}^{2})$$
From this point, the method for selecting molecules will depend on certain considerations such as your tolerance to variance and if you are more interested in the collective utility of your selection or if each individually selected molecule must meet a certain standard. If you didn't care about variance at all and simply wanted to maximize the collective expected utility you could bypass modelling utility as a random variable all together and stick with the first approach. An alternative if the variance was a factor would be to select the top 1000 molecules according to their mean utility, excluding molecules which didn't have a high probability of having a utility higher than some threshold $P(U &gt; C) &gt; 0.95$. These are just some examples, the exact approach will depend on your criteria which you need to clarify.
As to your question &quot;How would my protocol be adjusted if there was a constraint of diversity in the selected molecules&quot;. Diverse in what sense? Have you been provided with any other features to compare the molecules with or do you mean diverse in the three features already given? Again, another simple approach would be to append another feature calculated as the average distance to those molecules already selected.
One of the difficulties with your question is that it is very broad and open ended. There is not a lot of clarity surrounding what constitutes a good selection of molecules from a bad selection. For example, is it better to have a higher heuristic value 1 or a lower heuristic value 2? These sorts of questions need to be handled by a domain expert prior to applying the data science algorithm. If you were given a set A of 3 molecules and a set B of another 3 molecules do you have a clear way of determining which is the better selection? You need to be able to answer this question before you can begin applying any data science or else you are shooting in the dark.