So if you have your "objects" with coordinates in a list. You can easily bring them into ArcMap as a point feature class from csv, xls, mdb. Remember longitude = xcoord, latitude = ycoord. If you know the projection that the objects, you can set that, but it's not necessary. http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#//00s50000001z000000
If you know the object coordinates are in meters. You can then use the proximity toolset to find the objects within certain meters of a point. You might want to create a seperate point feature class that contains "start" points. http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/An_overview_of_the_Proximity_toolset/000800000018000000/
About projections... (you should probably read up on this), you say you have "objects" in a projected coord system (PCS). A PCS has a unit -- it is either feet or meters (it could be another linear unit but it's not) -- that is the projected unit. A PCS takes a round section of earth and flattens it to an xy plane. So if you have an input point, you need to use the same PCS to get a valid distance (distance will be in the PCS units) -- OR -- if you have an input point in geographic coordinates, you need to project it to your PCS before measuring distance to get a valid result.
If both are in geographic coordinates then you can do a geodesic length calculation. You need to make an API call to somewhere to get this. Or project them to a PCS for a simple calculation.
Btw, PCSs have very different characteristics depending on which PCS, and only some PCSs give good distance approximations e.g. State Plane. Google/Bing/Esri online maps, which use mercator, is extremely poor unless at equator.
First, given your experience level with GIS, are you sure you want to use ArcObjects directly? Learning curve is big with all the wrapped COM and huge API. Python scripting with the arcpy.py library is recommended for most automation scenarios. You may want to check that out. http://help.arcgis.com/en/arcgisdesktop/10.0/help/index.html#/A_quick_tour_of_ArcPy/000v00000001000000/
Second, one of the easier things to do in ArcObjects is to call the geoprocessing tools, like the proximity tools (but even easier with python). Fairly straight forward http://resources.arcgis.com/en/help/arcobjects-net/conceptualhelp/index.html#/How_to_run_a_geoprocessing_tool/0001000003rr000000/
Third, you could go the Geometry library and get closer to the bare metal with IProximityOperator, ITopologicalOperator, IRelationalOperator, etc http://help.arcgis.com/en/sdk/10.0/arcobjects_net/componenthelp/index.html#/Overview/002m0000047r000000/