As @EricShain has advised, an algorithm would be a utility patent.
However, if you are attempting to draft a non-provisional application for an algorithm without expert knowledge of Alice, Enfish, Bascom, and several key cases leading up to Alice, you're asking for trouble and putting the viability of the patent in great peril.
Even with extensive knowledge of these critical precedents regarding software patents you should use an experienced patent attorney who specializes in software patents.
For perspective, I was advised to file as a small entity as opposed to micro entity. The reason is that numbers like $130 vs. $65 are both trivial, and improper use of "micro-entity" status can be an avenue for challenge in the future, should you receive a grant. (Even if you fully meet the criteria, it doesn't mean someone won't use it as an avenue of challenge, forcing you to spend money to defend.
I'm not a patent attorney, but my advice is don't push it.
- File as small entity
The money you save filing micro-entity does not outweigh the risk. Apply minimax to your decision-making and weigh the future cost of a challenge against slightly higher fees today.
In terms of provisional/non-provisional, if budget is an issue, go for the provisional first. This gives you a kind of "blanket protection" for a year, and if you don't make a public disclosure, you can always refile a provisional at very low cost.
If you do make a disclosure, the provisional still protects you, but you will have no option but to file the non-provisional at the end of the year.
USPTO publishes non-provisionals about 18 months from the first filing (either the provisional or non-provisionals.) Provisionals without a subsequent non-provisional are discarded and never made public.
Note: Since there is some disagreement on the issue of provisionals, I feel the need to point out that provisional applications were introduced as a low cost route for inventors to gauge viability of a technology, and potentially raise funds, before committing to the expensive process of formally filing. I fear this aspect of the provisional application is all too often overlooked:
"Since June 8, 1995, the United States Patent and Trademark Office (USPTO) has offered inventors the option of filing a provisional application for patent which was designed to provide a lower-cost first patent filing in the United States..."
Source: USPTO "Provisional Application for Patent"
While it is always optimal to engage a patent attorney in drafting the provisional, it is not strictly necessary so long as you do your research and are thorough regarding what you include in the provisional.