OK,
@Davidasailor26 pretty much covered the solar controller. I'll only add a Victron 75/15 would be a good choice. It can handle up to 75v and 15a. That gives a little leeway on the 100 w panel.
Chargers should be sized based on the amphour (ah) capacity of the battery bank being charged. It is expressed as a percentage of the battery's capacity. A 1C charger will produce 100% of the battery's capacity, for a 100ah battery that would be 100a. Few batteries are happy being charged at that rate. LA batteries generally are happiest at .1C (10% of capacity) to .2C (20% of capacity).
So, the first step is to determine the capacity of the battery bank. The capacity of a Group 31 battery is around 100ah. A properly sized charger would be either a 10 or 20 amp charger. There are 2 advantages to going with the larger charger, it allows for adding an additional battery and recharging will be a little faster.
The charger should be a 3-stage charger with Bulk, Absorption, and Float stages. Ideally and for future proofing the voltages for each of those stages should be customizable. Some chargers will be advertised as a 20a two battery (or three battery charger). It is important to note the charger splits the charge current between the batteries attached to it, thus a 20a charger with 2 batteries will provide 10a to each battery or 20a to a single battery connected to the charger.
For your use a 20a charger should be adequate and a good choice would be a Victron charger. There are cheaper chargers on the market, however, Victron is a reliable company that builds good products. Companies like Renogy and Noco receive mixed reviews with the negative reviews being pretty strong. Sterling and ProMariner are also good brands, some of the chargers are the same, just different labels.