Travelling from outside Israel / Palestine you will most likely be flying into Tel Aviv (Ben Gurion) airport, a very modern airport situated approximately 45km North West of Jerusalem.
Following the formalities of Passport and Customs control, where you will be expected to request a travel Visa for entry to Israel see: VISA REQUIREMENTS ISRAEL you will have the option of SHERUT (shared taxi) or Egged BUS service from Tel Aviv to Jerusalem. Alternatively a TAXI will take you from the airport to the gates of the Old City.
Possibly the most economic, and convenient travel from the Airport to Ecce Homo is by SHERUT, a shared taxi service run by NESHER TAXIS. You will see their pick up stand just outside the terminal entrance. The service will not be able to drive into the Old City but drop you at either Notre Dame Hotel, Lions gate or Damascus Gate. From any of these places ECCE HOMO, on the Via Dolorosa is a short walk. Alternatively, a new rail service will take you, in comfort, from Tel Aviv airport (Ben Guiron) to the centre of Jerusalem at modest cost. The only downside is that the Rail Station in (Jerusalem - Yitzhak Navon) is a distance from the OLD CITY and Ecce Homo.However, if you are prepared to to take the LIGHT RAIL (Tram) from outside the Rail Station, with your cases, you will be at Damascus Gate and the entrance to The Old City in 6 tram stops. Alternatively, you can choose to take a taxi from the Rail Station to Damascus Gate or Lions Gate (nearest to Ecce Homo).