An iPad or other tablet, even used ones, will give you a decent moving map. Plenty of companies make radios and transponders, and I recommend getting a Mode S transponder one for future ADS-B connection. However, some ADS-B systems will operate with merely a Mode A/C transponder.
The ADS-B requirements are worth understanding, and some components like transponders or GPS work with only some of the other brands; the same holds for ADS-B receivers that display on a tablet. Some of the moving map apps only work with some of the receivers.
Another question is what to do about engine instruments. My preference is an electronic all-in-one system. These are usually called EMS for Engine Monitoring Systems and a variety of makes and models are available as stand-alone devices. In addition, most EFIS or Electronic Flight Information Systems can display all the engine data and do an adequate job of it. They almost all use an extra module of some sort to do that, so be sure to get that too if you go this route.
EFIS will provide far more than VFR data and in my own opinion are primarily desirable for IFR or with an autopilot.
Some EFIS will control or include a radio and/or a transponder. They will function as the control head. Since some radios and transponders allow (or even require) that, this compatibility could affect your choice of radio or transponder.
The choice of battery will be determined first by whether you have a starter or not, and if so, there are numerous options. Many of these options are lighter than what was available when the RV-3 was designed, and some come with safety issues. Be certain that you understand those if you choose them. If you're not going to have a starter, then the battery will be at least partly determined by the current draw from the radio and transponder.
The larger EFIS systems barely fit an RV-3. In any event, I recommend printing full-size photos of the various components that will go on the panel and fitting them to the panel before purchasing. Some builders have made the panel slightly higher for additional space (by keeping the upper contour but letting the bottom move downward) and others have added center stacks between your feet for more equipment. These usually connect to the F-312 assemblies. Builders have also installed small equipment on the right side panel.
1. Determine what requirements you have.
2. Decide upon an architecture.
3. Assess compatibility between systems and devices.
4. Narrow down the many choices by seeing what will fit and what meets your requirements.
5. Study the installation and operators manuals (most are available on line) and use this to further narrow the selection.
6. Iterate as needed.
Good luck!
Dave