How can I purify Ferric or Ferrous acetate with a very basic lab?
Both the Handbook of Chemistry and the Merck Index state that $\ce{Ferric Acetate}$ exists only in solution. If this solution is evaporated, a basic ferric acetate is obtained that is insoluble in water, with a formula $\ce{Fe(OH)(CH_3COO)_2}$. This basic acetate is soluble into acetic acid.

Nevertheless there has been recent reports stating that solid Trinuclear Ferric Acetate may be obtained in rather concentrated solutions with the following structure : $\ce{[Fe_3O(OAc)_6(H_2O)_3]OAc}$. Its synthesis has been described in A. Laurikenes et al., Lithuan. J. Phys. 56, 1. p.35 (2016). 
They mix $11.2$ g Iron powder ($0.200$ mol) and $12$ mL $\ce{CH_3COOH}$  $50$% ($0.100$ mol) at $75°C$. Why this choice ? The contrary would have been a much better choice (interchange $0.1$ and $0.2$)... They obtain a concentrated green solution, which they filtrate, and they add $6$ mL $\ce{H_2O_2}$ $30$%, and filtrate the obtained red mixture. The obtained filtrate is very concentrated. It is then evaporated under vacuum. And they obtain $2.95$ g of the trinuclear compound. The yield is miserable.  But they say that they have been able to recrystallize this compound in ethanol. 

It is interesting to know that this substance has three equivalent $\ce{Fe}$ atoms in the apexes of a triangle, with an Oxygen atom in the center of the triangle, and that each $\ce{Fe}$ atom is included in the center of an octahedron, where all apexes are occupied by Oxygen atoms. 

See also : K. I. Turte et al. Synthesis and Structure of Trinuclear Iron Acetate, J. Struct. Chem. 43, 108-117 (2002)